Leo Goodwin Jr., 63, head of a financial empire that includes the Government Employees Insurance Co. (Geico), died Sunday in Fort Lauderdale, Fla. He was hospitalized more than two months ago with cancer.

He was the son of Leo Goodwin Sr., founder of Geico, who died in 1971.

In May, 1976, the younger Mr. Goodwin filed one of the largest personal bankruptcy petitions on record in the wake of the large automobile insurance firm's financial woes.

According to papers received at the Federal Bankruptcy Court in Hyattsville, Mr. Goodwin had assets of $26.55 million and debts of $29.99 million.

Mr. Goodwin, who had homes in Potomac, and Fort Lauderdale at that time, filed the petition seeking court protection for his remaining assets as well as personal property while he attempted to reorganize his debts.

Ten days later, he also stepped down as a member of Geico's board of directors. He had been a director since 1948.

He also had served as a director of Geico afifliates in life insurance, consumer finance and high-risk auto insurance, owning a substantial bloc of shares in each of those firms as well as in Geico.

Geico was having financial troubles at the time. For the past year, it reportedly has been experiencing a strong recovery.

Mr. Goodwin grew up in Texas, where his father and a banker founded Geico as a Texas corporation in 1936. The company was incorporated in the District of Columbia the following year and become Washington's largest automible insurance firm.

A graduate of George Washington University, Mr. Goodwin had been a paratrooper in World War II. Last June, his son, Leo III, died of a drug overdose.

Frances B. Goodwin, who was divorced from Mr. Goodwin in 1974, asked yeaterday that expressions of sympathy might be in the form of contributions to the Leo Goodwin Institute for Cancer Research.