Government Employees Insurance Co. chairman John J. Byrne said yesterday that his company may roll up record profits in 1977.

Speaking to stockholders of the automobile insurance firm at the annual meeting here, less than a year after Geico appeared headed for insolvency, Byrne said:

"Wouldn't that be something, to have the company make its highest profit in history the year immediately following the cliffhanger?"

Specifically, Byrne poured cold water on some published speculation that Geico's profits could be $100 million this year - estimates based on the company's recovery from loss operations and net profits for the final two quarters of 1976.

"I want to tell you loud and clear that I don't see that in the cards," he stahe fourth quarter and multiply it by four, you get about $98 million, which by coincidence happens to be Geico's largest profit in history. I think the 1977 net income could well be better than that," compared with a 1976 loss of $26 million and a 1975 record loss of $126 million, Byrne told more than 300 stockholders.

The setting for the happy forecast, which obviously pleased those in the audience, was appropriate. Byrne and his associates were seated on the stage of the Kennedy Center's Eisenhower Theater, in the middle of the set for the final scene of the hit musical, "Annie," which happens to have a very happy ending.

Where cartoon stip business tycoon Daddy Warbucks nihtly recalls how he used to turn a million dollars into $100 million, Byrne said yesterday that he has a dream for Geico based on a mood of "seriousness, stability and prudence" - words that a Warbucks would like.

The dream of Byrne is to make of once-sick Geico a company expanding its auto insurance business and adding new lines of insurance and financial services.

But that won't come for sometime, he told the stockholders."This is strictly a secondary priority. Where we live for the next two years is that block of automobile insurance business" that Geico now has.

Sharp rate increasses last year and bad publicity about Geico drove away preferred-risk customers the comapny "would have preferred to keep," he said. In recent months, Washington-based insurer has restructured rates in many states to provide lower premiums of customers with the safest driving records and Byrne said his goal for 1977 is to add 150,000 new policies.

Last year, Geico lost 700,000 policies, "a moderately unafavorable variance from our plan," he said. But it was necessary to move fast with a three-pronged program designed to keep Geico alive - the sale of $75 million of preferred stock, most of which was picked up by current stockholders (a reinsurance "treaty" under which competitors assumed the loss risk for 25 per cent of Geico policies; and "operation bootstrap," under which the firm cuts its staff and its number of customers.

The profits forecast for 1977 will include a "moderate" profit from under-writing insurance, Byrne said, in contrast to losses that continued through the end of 1976. In addition, the company has $137 million of tax loss benefits to apply against profits and Byrne said Geico plans to use that amount in the next three years.

Stockholders, meanwhile, voted to increase the par value of Geico stock back to $1 a share from 10 cents, reducing the statutory surplus account by $16 million to $111 million. They also elected one new director, University of Chicago professor and consultant H. Edward Wrapp.

Following the Geico meeting, stockholders of three affiliated firms held their annual sessions. Highlights of those meetings included:

At Government Employees Life Insurane Co., a review by president Thomas R. Hefner of difficulties faced in erasing the problems of Geico from Government Employees Life, an independent company with separate management, because of "negative publicity" and the fact that news media have "exercised greater restraint in publicizing the solution that they did the problem."

Gelico individual life sales were down 22 per cent last year but Hefner said recent results look encouraging - February life applications were the highest since last June and voluntary terminations for the first two months of 1977 are down 10 per cent under the average for the final four months of 1976.

At Criterion Insurance Co., an auto insurer that accepts higher-risk customers than Geico, a moderate underwriting profit was recorded in the first two months of 1977.

At Government Employees Financial Corp., credit volume was up slightly for the first two months and profits dipped slightly to $638,000.