It looks like any other office in any of the other new buildings that have sprung up recently on Houston's booming northwest side, and inside it is the model of a modern operation, complete with computers and the scent of busy copying machines.

But the unobtrusive name on the door suggests that something more than the ordinary devotee of free enterprise operates within. This is the command post for organized labor's effort to crack the Sun Belt.

Labor calls it the Houston Organizing Project, and with a budget of $1 million and a staff of 20 organizers, it is the AFL-CIO's biggest effort in the fast-growing and traditionally anti-union states of the South and Southwest.

"We couldn't stay in our comfortable home in the Northeast and Midwest forever," said Charles McDonald of the AFL-CIO's organizing and field services department in Washington.

Over the years, organized labor has watched the flow of industry and workers from the well-organized North to the unorganized South. Only 13 percent of the work force is unionized in Texas, which ranks 47th among the states in the percentage of unionized workers.

Moreover, unions are finding it more difficult to win representational elections in states like Texas. In fiscal 1980, it won just 44 percent of the 201 elections held under the auspices of the National Labor Relations Board. The result is that labor is falling farther and farther behind the growth of the labor force, even though its membership rolls in Texas continue to grow.

If labor succeeds in Houston, it may expand its organizing efforts to other major Sun Belt cities.

On the advice of labor officials in the Houston area, the AFL-CIO got various international unions to commit the money for the first year of an organizing drive, drew up a plan modeled on the successful Los Angeles Organizing Project launched in the early 1960s, and set to work.

"They drew the blueprint in Washington," said Bob Comeaux, 34, project director here. "We're the craftsmen who put it together."

Houston was chosen because of its growing economy and because local organizers suggested there was growing interest in unions among unorganized workers.

The unions decided not to go for a big, splashy organizing effort aimed at one of the major non-union firms in Houston. Instead, they are responding to a backlog of about 80 requests for help in unionizing various smaller companies in the area.

Comeaux said that to date the organizers have added about 2,000 workers to the union rolls, won one representational election at a small export company and prevented a decertification effort at another firm. But the AFL-CIO's McDonald acknowledges that the project "hasn't leaped off the floor."

The unions are organizing in hostile country. Texas, like many states in the Sun Belt, is a "right-to-work" state, which means it prohibits closed shops. (Closed shops are operations under a contractual arrangement between a union and employer by which only union members may be employed.) That shuts off labor's easiest avenue to organizing, says an opponent of the unions.

In addition, firms in the Houston area are gearing up to stop the AFL-CIO drive. The Associated Builders and Contractors has held two seminars for member companies in the past few months, showing them how better to compete against unionized firms.

MedeX, a consulting and placement firm here that helps hospitals and health care companies avoid unions, has been contacted by some new clients who are worried about the AFL-CIO's operation.

Comeaux readily admits that the climate in Texas makes his work more difficult. "There are a lot of leeches down here, union-busters who like to go out and kill something," he said.

But William Brown, chairman of the legal rights and strategy committee of the Houston Associated Builders and Contractors, said the unions' problem is simply that the workers don't want to join.

"There's no need for unions," Brown said. "The employes of companies that are not members of these associations have never felt they have any advantage to gain by joining a labor union."

Comeaux said a member of the Houston ABC told him the association has a $2 million war chest to help companies blunt the AFL-CIO's drive, but Brown denies it. "They've got a right to organize," he said.

But he also made it clear he thinks unions are an evil influence. "Most of the northern states are not right-to-work states," he said, "and most have a long history of union domination, corruption, violence, sabatoge and mass picketing. The first step is to control politics. If they can elect all the local sheriffs and chiefs of police and judges and district attorneys, they can coerce and compel employers to sign pre-hiring agreements. You don't have that sort of situation in Houston."

Don Crow, vice president of MedeX, added, "For many years, Texas and the Houston area have been growing very dynamically and doing it without union representation. Generally, people feel that the employer-employe relationship can work effectively without third-party representation."

Despite the Sun Belt's history of anti-unionism, Comeaux believes that is changing in favor of the unions. "I definitely believe that the workers of the Sun Belt are being victimized and that they're rapidly awakening to that fact."