Safeway Stores Inc., the nation's largest food retailer, reported yesterday a sharp increase in profits for the quarter and full year ended Dec. 30.

Earnings for the food chain, which is one of the two largest supermarket operators in metropolitan Washington, were a record $146 million ($5.60 a share) in 1978 compared with $102 million ($3.93) the previous year. Sales rose 11.6 percent to a record $12.6 billion.

For the fourth quarter, Safeway earned $47.9 million ($1.83 a share) on sales of $3.9 billion compared with profits of $32 million ($1.22) and sales of $3.6 billion for the 1977 period.

Safeway, based in Oakland, Calif., said the 1978 earnings reflected losses of foreign currency transactions of $7.9 million (30 cents a share) while the 1977 operations included a smiliar loss of $3.25 million.

In addition to its 2,000 U.S. stores, Safeway operates 274 food outlets in Canada, 83 in Britain, 60 in Australia and 26 in West Germany.

During the past year, Safeway opened 111 stores (99 in the U.S.) and closed 103 smaller, outdated units (92 in the U.S.). The average size of new stores opened was 35,200 square feet.