Government Employees Insurance Co. one of metropolitan Washington's largest private employers, yesterday began a new program designed to reduce its work force, through voluntary "furlough," by year's end.

An announcement to all salaried employees of the large automobile insurance firm said business expansion to date in 1977 has been less than projected and that the work force also must be smaller."

Since the end of 1975, when financial difficulties began to threaten Geico's survival, the company has trimmed its work force by 25 per cent nationwide. At the end of August, the firm employed 5,500 persons - some 3,500 in the Washington area alone.

Over this same period of time, Geico's insurance policies in force declined by 40 per cent. As part of a survival program, new management at Geico cancelled some customers deliberately to reduce expenses and losses from claims, other customers of Geico switched to competing firms.

Although the Chevy Chase-based firm has started to seek new business again, a spokesman said yesterday that the marketing effort was slow in starting.

Chef operating officer Edward S. Ring linked the staff cut with the smaller number of policies in force needing to be processed. He declined to state a specific number but indicated that management hopes "a relatively small number" - less than 250 persons - will take advantage of the furlough program outlined yesterday.

Geico's memo said all workers with 10 years or more total employment in Geico and its three affiliates may apply this month for the furlough program - essentially a voluntary layoff with no expectation of being recalled. These workers would receive, in exchange, a payment equal to two weeks of salary for the first year employed and one week for each year thereafter.

Thus, a Geico worker with 11 years of employment who elects to seek a furlough could receive 12 weeks' pay. The company said it would retain a right to reject any application for furlough and would set the date for leaving the company. Workers also could combine furloughs with retirement, Geico said.

Ring noted that Geico has been reducing its employment gradually through normal layoffs. He described the new plan as a "somewhat generous" attempt to offer people not next in line for layoff the opportunity to leave or retire.

In mid-August, Geico announced that a projected recovery was advancing "essentially according to plan." The company had planned to add up to 100,000 customers this year, but policies in force continued to decline at a slow rate through June 30.