The Prince George's County Board of Education, which hasn't built a new school since 1978, is proposing to build three, although the system is still beset by problems of falling enrollment and tight budgets.

The new buildings would replace four schools--three of which are the oldest in the county--and new construction rather than consolidation is proposed because the schools serve communities the board considers stable and where the birthrate is expected to remain high. Replacement would be cheaper than renovation, school officials said, because the structures have deteriorated and it would be costly to bring them up to current building code standards.

The construction would cost at least $15 million and probably wouldn't begin for seven years.

The board set Aug. 15 for a public hearing on the proposal to:

* Replace Bladensburg Elementary School, which was built in 1939, with a new building on the grounds of Bladensburg Junior High.

* Build a new school to replace Cheverly-Tuxedo and Happy Acres elementaries, both of which are in Cheverly. The new school would have a capacity of 600 pupils; the two existing ones are expected to enroll 410 this fall and about 500 by 1992. Cheverly-Tuxedo was built in 1922 and Happy Acres in 1955.

* Replace the 46-year-old Greenbelt Elementary, incorporating and renovating an addition built in 1968.

The last school built in the county was Riverdale Elementary, in 1978.