A federal judge in Alexandria yesterday transferred the criminal fraud trial of Litton Industries, charged with claiming $37 million in improper shipbuilding charges, from Virginia to Mississippi, where the vessels were built.

U.S. District Court Judge Albert V. Bryan Jr., whose dismissal 18 months ago of the charges against Litton was overturned on appeal, said he hesitated to "shuck on someone else my responsibility...," but said the interests of justice and convenience to Litton warranted the transfer.

Bryan ordered the transfer at the request of Litton and despite arguments against it by the Justice Department.

A federal grand jury in Alexandria indicted Litton, a major defense contractor, in April 1977 on the charge of fraudulently overcharging the Navy for building three nuclear attack submarines between 1968 and 1971. In May 1977, Bryan dismissed the indictment and ruled that government prosecutors "behaved badly" during preindictment negotiations with the contractor.

Last April, however, the 4th U.S. Circuit Court of Appeals reversed Bryan. It relied upon a Supreme Court decision on plea bargaining that was handed down after Bryan's dismissal of the indictment. The Supreme Court in October declined to hear Litton's appeal of the 4th Circuit Court's ruling.

Because disputed Navy shipbuilding claims amounted to more than $2 billion industrywide, the 4th Circuit ruling took on major importance to the nation's shipbuilders. Since then, Congress has agreed to pay $978 million in other cost overrun claims to Litton's Ingalls Shipbuilding Division and to the Electric Boat Division of General Dynamics in Connecticut.

The Navy said the settlements, the result of months of negotiations, will avoid years of court fights and possible disruption of shipbuilding.

In a hearing yesterday David H. Pittinsky, a lawyer for Litton, argued that the trial should be held in the Southern District Court of Mississippi because the Ingalls Division, where the contested vessels were built, is in Pascagoula, Miss.

Pittinsky also argued that possible witnesses are near Pascagoula, as are documents and records involved. Pittinsky said a trial in Virginia would disrupt Litton's business and would be expensive.

Joseph Fisher, one of the assistant U.S. attorneys criticized by Bryan in his dismissal opinion, argued yesterday that because Litton submitted the charges to Navy officials in Virginia the trial should be held there. He also argued that the transfer could further delay the trial.

Fisher said one Litton official who was to be a government witness has died. Most of the government's witnesses live in the Southeast and the trial is not expected to be lengthy, Fisher contended.

Bryan said his decision relied on part of his May 1977 decision in which he had said he probably would transfer the case if it came to trial. In his opinion, Bryan agreed with most of Litton's contentions of inconvenience and expense and said that the indictment was handed down in Virginia because the Navy office "by mere happenstance is located here."