Giant Food could open as many as 12 new stores by February 1980 and is trying to cut the cost of building a new store by 20 percent, stockholders were told at the company's annual meeting yesterday.

One reason for the expansion push is that four stores originally scheduled to open during the current year are behind schedule. But others are moving ahead rapidly. David B. Sykes, senior vice president for finance, told shareholders yesterday.

Sykes said Gaint will invest $38 million in expansion during the current fiscal year, spending $27 million on new stores, remodeling and expansion of existing stores as well as the installation of computerized checkouts. All stores will have computer checkouts by 1981, making Giant the first food chain to be completely computerized.

Also in that budget is $6 million for warehouse expansions and construction of a new high-rise frozen food warehouse at the company's Jessup, Md., distribution center where the annual meeting was held.

Another $5 million is to go for processing plants, including construction of an ice cream making factory at Jessup, said Samuel Thurston, vice president for distribution. A new meat and delicatessen warehouse are also planned, along with a new fish warehouse.

E. Douglas Kelbaugh, the vice president for construction, said staffers are working on "Project Spartan" aimed at cutting 20 percent from the cost of new store construction and fixtures, which now add-up to $2.2 million per unit.

New Giant stores will be expanded from the current 39,000 square feet to 45,000 sqaure feet, added Kelbaugh during a series of reports by six Giant vice presidents.

The vice presidential presentations were criticized by activist stockholder Evelyn Y. Daivs, who told Giant President Israel Cohen he should be talking to the stockholders himself.

Davis peppered Cohen with questions for almost half an hour and was booed by other shareholders after she admitted she usually shopped at Safeway.