The nation's leading insurer of general aviation aircraft expects broader use of private airplanes during a future era of energy-consciousness to create increased business opportunities.

Avemco Corp. chairman Arnold H. Johnson, addressing his firm's stockholders at the annual meeting in Bethesda yesterday, said that since scheduled airlines serve only 425 of the nation's 12,000 airports, general aviation will be used increasingly to "fill the gap," particularly for business travel.

Use of private planes is "more cost-effective and fuel-efficient" than automobiles and has become a necessity for some companies, Johnson said.

Stastistics published separately by the General Aviation Manufacturers Association show that the first quarter of 1977 broke all records for shipments and billings. Shipments totaled 4,123 units in the quarter, up 4.4 per cent from the same period last year. March was also the biggest single month on record for the industry.

Avemco's profits in the first quarter were a record $528,790 (18 cents a share) compared with $329,494 (11 cents) in the 1976 period and Johnson said yesterday the first-quarter results point to a 20 per cent gain in profits over the full year. In 1976, Avemco earned $2.07 million (a record 70 cents a share).