A federal grand jury in Alexandria yesterday indicted Litton Industries, a major national defense contractor, on a charge of fraudulently overcharging the Navy $37 million for building three nuclear submarines.

The indictment charges Litton with falsely submitting a claim to the government when one of its divisions, Ingalls Nuclear Shipbuilding of Pascagoula, Miss., gave the Navy a 42-page explanation of costs in building the submarines. Ingalls said delays by the Navy caused the company to subcontract part of the work and disrupt its schedule.

The government charged in the indictment that the cost data were "false, fictitious and fraudulent," and contained "misrepresentations and omissions of material facts."

Ingalls said yesterday in a prepared statement that "it is innocent" of the government's charges and that the incident "is another example of that Navy's mismanagement of its claims settlements in its shipbuilding programs . . . We are convinced there is no fraud in our claim."

The investigation into the charges was started in January, 1974, by the Justice Department after the Navy tried to determine how much of the cost over the original $100 million contract it was obligated to pay Ingalls, according to Special Assistant U.S. Attorney Richard D. Kibby.

The grand jury first heard testimony in November, 1974. The case was heard in Alexandria because the claim was sent to Navy offices in Arlington, Kibby said.

The Navy first entered the contract for the three SSN-680 submarines June 25, 1968, according to the indictment.

The first submarine was supposed to be delivered to the Navy in September, 1971, but the Navy postponed delivery a year because it was unable to ship steel to Ingalls on time, Kibby said.

Ingalls then said that to keep costs down due to the delay, it would stretch out the shipbuilding time rather than delay the start of construction, the indictment stated.

Ingalls claimed that the Navy was late in delivering steel, causing Ingalls to subcontract part of the work. Ingalls eventually said it had to subcontract part of the construction three times because the Navy's delays disrupted its schedules with other contractors.

On Nov. 30, 1970, Litton submitted to the Navy the $37 million claim and an explanation of the costs, the indictments said.

Litton, a Beverly Hills-based firm, receives about one-third of its $3 billion annual revenue from national defense contracts, according to a Litton spokesman. The company also manufactures typewriters and microwave ovens.

The Navy already has paid Litton about $3.5 million of the additional charges, according to Assistant U.S. Attorney Frank W. Dunham Jr. The submarines have been operating in the U.S. fleet for two to four years, the Litton spokesman said.

Neither Kibby nor Dunham would say how they knew the charges were deliberately false and not an oversight by Ingalls. The penalty for submitting a false claim to the government is $10,000, Kibby said. Recovery of any money paid because of fraudulent claims could be recovered by filing a civil suit.

Ingalls also said yesterday it is seeking from the Navy $13.6 million due on a $17.3 million judgment it said it was awarded by the Armed Services Board of Contract Appeals in April, 1976 inconnection with the SSN-680 submarine contract. Ingalls said payment of the award was held up by the Justice Department investigation into the claims.