Marriott Corp. plans to become the fourth-largest hotel chain in the United States by 1985, President J. W. Marriott Jr. told stockholders at the company's annual meeting yesterday.

Now ranked 11th-largest in the domestic lodging business, Marriott will open 22 additional hotels this year and is scheduled to expand by 20 to 25 percent a year, hitting 150 hotels and 70,000 rooms by 1985, he said.

"We'll continue to expand our strong presence in the Sun Belt, in medium-sized cities and other markets where the demand for quality hotel rooms exceeds the supply," Marriott asserted.

"We'll selectively build large hotels in major U.S. cities," including Washington, where work is under way on an 830-room hotel on Pennsylvania Avenue adjacent to the National Theatre, he added.

This year's Marriott meeting was held at the Twin Bridges Marriott, which opened 25 years ago as Marriott's first hotel. Marriott was a $29 million-a-year business then, and last year sales were $1.7 billion. In 1981, the company will become a $2 billion-a-year business.

A single share of Marriott stock was worth $16 back in 1957, Marriott noted. After stock splits and stock dividends, that share is worth almost $1,200 today.

Marriott Corp.'s goal for the '80s is to increase profits by 20 percent a year and maintain a 20 percent return on stockholders' equity, he added.

"We expect the company to have a good year in 1981, considering the relatively slow progress of economic recovery," Marriott said. "We believe that 1982 will be a much better year for us and our business than either 1980 or 1981."

During a question-and-answer session, the Marriott chief executive said the company has abandoned consideration of building a major theme park in the Washington area because "the capital outlay and the competition are too great."

The company had considered putting a park somewhere in the Washington-Baltimore corridor similar to the ones it runs in Illinois and California, but "right now that is a closed issue," Marriott said.

Marriott will not give up its Hot Shoppes and Hot Shoppes cafeterias, however, he assured an elderly stockholder who said those operations are a favorite economical eatery for senior citizens.

The decline in traffic at Dulles International Airport has hurt Marriott's terminal restaurants there and cut volume of the airline kitchen the company runs at Dulles, but the Dulles Marriott is prospering, he said.

Getting down to meat-and-potatoes issues, the Marriott president said there is a very simple reason why Roy Rogers restaurants don't offer fish sandwiches like McDonald's: "They don't sell."

He said first-quarter profits were up for Marriott's restaurant division, and "trends are encouraging, particulay in our major Roy Rogers and Big Boy markets."