James A. Buford, a 43-year-old health administrator, was nominated yesterday by Mayor Marion Barry to head the city's massive and troubled Department of Human Services.

The appointment means that for the first time Barry will have a director of his own choice in charge of the agency, which has come under frequent criticism for inadequate delivery of health care and lax management of the welfare program.

Buford, currently regional director of health services for the U.S. Department of Health, Education and Welfare in Dallas, appeared with the mayor at a District Building press conference and said he does not promise "instant solutions" to the problems at DHS.

But City Administrator Elijah B. Rogers, who conducted the search that led to Buford's appointment, said Buford fits in with the Barry administration's theme of "can-do" self-confidence.

Before accepting the post in Dallas last September, Buford was HEW's chief troubleshooter at St. Elizabeths Hospital, the federal psychiatric facility in Southeast Washington.

Before that he was director of the smaller Newark N.J., social services agency. DHS, with more than 8,000 employes and a total budget of more than $440 million -- almost a third of the city's entire budget -- is the largest District department.

If he wins confirmation by the City Council, Buford will become the third director to head the agency since it was established as the Department of Human Resources eight years ago by then-mayor Walter E. Washington in a consolidation of various health and welfare agencies.

Washington appointed Joseph P. Yeldell to head the agency. Yeldell's stewardship was stormy and scandalplagued, however, and in 1976 Washington replaced him with veteran administrator Albert P. Russo, who is retiring today.

Russo's quiet style was vastly different from Yeldell's but the agency continued to come under criticism from mayoral task forces, congressional auditors and District residents who use its services.

The agency has had serious problems in monitoring its welfare payments, has been accused of some responsibility for the District's tuberculosis and infant mortality rates, and has been widely criticized for maintaining substandard facilities.