President Reagan yesterday nominated Judge James A. Belson, who has served 13 years on the D.C. Superior Court bench, to the D.C. Court of Appeals, the city's highest appellate court.

Belson, 49, who would succeed the retired Judge George R. Gallagher, must be confirmed by the Senate. He would join a court that has been shaken by dissension in recent years, including an unsuccessful attempt last fall by four judges -- including Gallagher -- to strip Judge Theodore R. Newman Jr. of the court's chief judgeship.

Belson, who once was under consideration to be chief judge of the Superior Court, is a widely respected legal writer and jurist. He was appointed to the trial court in 1968 by President Johnson. He was reappointed in 1978 after receiving a rating of "exceptionally well qualified" by the Judicial Tenure Commission, the highest ranking given by the city agency that reviews the qualifications of sitting judges. Belson presently heads the Superior Court's civil division.

Born in Milwaukee, Belson moved to the Washington area at the age of 12. He attended Gonzaga High School and Georgetown University, and graduated from the Georgetown Law Center in 1956. He served in 1956-57 as law clerk to U.S. Court of Appeals Judge E. Barrett Prettyman, and later was a partner in the Washington law firm of Hogan & Hartson.

Among Belson's most noteworthy cases was a ruling that led to stricter controls on creditors under the city's wage garnishment laws, and a test case in which Belson ruled that it was not unconstitutional to charge heroin addicts with possession of heroin for their own use.

Belson recently heard arguments in the pay-raise dispute between city employes and the mayor, and is expected to rule on the issue before leaving the trial court.

The White House is expected to name three judges soon to fill vacancies on the D.C. Superior Court, and eventually also must name a successor to Belson on that court.