Highway construction costs dropped by 8.4 percent in the first three months of this year, the largest quarterly decline in more than 30 years, the Transportation Department said yesterday.

Although highway costs are traditionally down in the winter months, the sharp decline this year is particularly noticeable because it follows a series of dramatic increases in 1978. Costs rose 2.2 percent in the last quarter of 1978, following record quarterly increases of 14.7 percent and 17.6 percent.

Transportation Secretary Brock Adams ordered last November that any federally aided highway project exceeding its estimated cost by more than 7 percent be reexamined and possibly rebid.

Adams says the first-quarter returns show his program taking hold: "I am pleased. The government should not be contributing to inflation, but rather pressing it back."

From January through March, 1,356 federal aid projects were advertised for bids by state highway departments, according to the DOT. Bids on 290 of those contracts exceeded engineers' estimates by more than 7 percent. Fifty-seven bids totaling $76.7 million were rejected, and the projects were readvertised after review. Eight of those projects have been rebid, according to the DOT, and savings of $3.5 million resulted.

The Federal Highway Administration's composite price index of highway construction costs closed at the end of the first quarter at 277.2 percent of the 1967 base index. In other words, it costs almost three times as much to build a highway today as it did in 1967. CAPTION: Picture, MATHIAS J. DeVITO . . . predicts record year