Fairfax County dedicated a new shelter for the homeless yesterday, and officials were quick to predict that its 60 beds will be filled by Christmas.

The North County Community Shelter in Reston is the third such facility in Fairfax County, an area not generally thought of as having a growing homeless population. Nevertheless, officials estimate that 2,500 people were turned away for lack of space at county shelters in fiscal 1987.

"There are many people who find it very difficult to believe we have a problem," Martha V. Pennino, vice chairman of the county Board of Supervisors, told a group of about 100 people who gathered for the dedication of the new shelter, which is in Pennino's Centreville District.

While the ceremony was tinged with concern about the future, there was pride in the fact that 60 additional beds are now available for those who have no place else to go.

"You are a group of people who recognize a need outside yourself," Pennino told the crowd. "You didn't fight and say, 'Not next door to me.' "

The 9,600-square-foot shelter at 11975 Bowman Towne Dr. is next to the Reston Regional Library.

With its vaulted ceilings, patios and dusty rose miniblinds, the shelter blends right into one of the nation's best known planned communities and could easily be mistaken for a contemporary recreation center.

With the shelter's completion, Fairfax County now has 262 beds available for the homeless, said Peter Gray, the county's emergency housing administrator. Similar shelters are located in the southern part of the county and in the Baileys Crossroads area, and there are two smaller family shelters, Gray said. In addition, as many as 150 people are put up by the county in motels every night, he said.

The $1.4 million North County shelter, on which construction began last December, opened its doors to a few homeless people on Monday. It has separate wings for singles and families, said Gray, who predicted that both will be full for the first time by Christmas.

The county's shelters provide year-round emergency housing, food, clothing and a range of counseling services from private and county staff, he said.

Gray said the typical homeless person in Fairfax County is a white male in his early twenties, with substance abuse or mental problems. He said about 35 percent are employed but cannot afford housing.

Eric Goplerud, an assistant professor of psychology at George Mason University and one of yesterday's speakers, said the problem of homeless families in Fairfax is increasing, and that the county needs three or four more shelters to serve them.

In a survey in March, Goplerud said, he counted 654 homeless people from the county in just one day.

Others in the Washington area have found that number "inconceivable," he said, mostly because when they drive around the county they see affluence, not homelessness.

"It's not the same as in the District because you don't have people sleeping on grates," Goplerud said. "But if you look around, you can see them sleeping in the woods."

Gray said that while no other shelters are under construction in the county, the problem is being studied by a task force.