Overwhelmed by the massive immigration that is changing the face of the western United States, this city moved closer tonight to putting its public schools on a year-round schedule.

Despite widespread public opposition, the school board voted 5 to 2 to authorize planning to eliminate the traditional summer vacation in order to make room for an anticipated 82,000 additional pupils in the next five years.

"It is not possible to construct new schools rapidly enough," Superintendent Harry Handler told the board, nor was it expected that a legislature frightened by recent tax revolts would appropriate the money.

Los Angeles would be, by far, the largest district in the country to go to year-round schools, in which a staggered vacation schedule at each school ensures that all its students never are present at one time. The system has been popular in some mushrooming suburban areas unable to keep up with the demand for new classrooms, but no large city has instituted the program to the extent that Los Angeles is planning.

Prince William County, Va., experimented with year-round schools in the 1970s but largely abandoned the system in 1979. In reverting to a nine-month academic calendar, school officials said that the year-round schedule had proved exhausting for many teachers and a scheduling nightmare for administrators.

In Los Angeles, the idea has revived some of the ethnic and racial tensions felt during the city's long desegregation crisis. White parents in the suburban San Fernando Valley have objected strongly to the potential disruption of family vacations, special courses and after-school sports.

"These are the strongest feelings about a school policy that I've seen since the busing issue," said David Armor, a school board member from the valley who voted against the plan. Some parents, he said, might abandon the public schools, as many did during the period when many whites were bused to achieve racial balance in the schools.

Alan Gershman, a member from West Los Angeles who voted to begin the year-round planning, said 99 percent of those he spoke to opposed the idea, but he saw no feasible alternative with an annual increase of 14,000 pupils.

"This problem is going to spread across this state," he said.

Immigration, along with a national spurt in birth rates and strong anti-tax sentiment, has left schools here struggling to educate 574,233 pupils and facing the prospect of not enough space for the approximately 660,000 expected in 1991.

Immigration from Latin America, both legal and illegal, has produced a student body that is 53.7 percent Latino. Asian immigration, particularly from Hong Kong, Taiwan, South Korea and Vietnam, has swollen the number of ethnic Asian pupils to 8.2 percent, while the numbers of blacks (19.2 percent) and Anglos, or non-Hispanic whites, (18.7 percent) have stabilized or declined.

Not only has the number of Latino families in Los Angeles increased, "but traditionally, Hispanics have larger families," noted Bill Rivera, assistant to the superintendent. And the rising costs of private schooling, even in church-subsidized Roman Catholic schools, have forced many families to send their children to the public schools, said Rivera, who recently served on a church commission analyzing the shrinking enrollments at local parochial high schools.

A recent Rand Corp. study concluded that Latino immigrants to California pay more in taxes than they receive in welfare and health services, but noted that they place an added burden on the public schools.

Many of Los Angeles' predominantly Latino neighborhoods already have year-round schools, Rivera noted. About 100,000 children at 93 schools in the most crowded parts of the city live with staggered vacations.

Several parents from areas currently on the year-round system objected today to the board's plan to force them to change their vacation formula to match a new formula for the rest of the city. The board agreed to try to be flexible in meeting their needs, but did little to ease the fears of many parents that family schedules would be severely disrupted by the new system.

The board also agreed, in principle, to spend $290 million for air conditioners so students would be able to concentrate on lessons in the hottest part of summer. The resolution indicated the board would begin the year-round program in schools without air conditioning only if there was no other way to find space for all students.

School officials indicated that the air-conditioning requirement may delay implementing the year-round program until 1988 at the earliest. Handler said that he expects the board to vote on a specific year-round plan next month.