The unemployment rate in Maryland rose to 7.9 percent in December, an increase from November's 7.7 percent, the state's Department of Health and Human Services reported yesterday.

Nevertheless the December rate was well below the prevailing national average of 10.8 percent in the final month of 1982 and lower than the 8 percent unemployment rate the state recorded in December 1981. Mary Corddry, an economist with the state, said Maryland's unemployment rate improved over most of 1982.

The unemployment rate reached its peak of 9.8 percent in January 1982, she said. "We started pulling out of the recession before" the national economy, Corddry said.

She said the state has experienced employment gains in trade and service industries and that employment in other industries has held its own.

Yesterday, the Department of Labor reported the first hopeful news that the nation is recovering from the worst recession since the Great Depression. The department said the nationwide unemployment rate fell from 10.8 in December to 10.4 percent in January.

Unlike the national unemployment rate--which is adjusted to account for regular seasonal employment patterns such as heavy pre-Christmas retail hiring or the spring influx of students into the job market--the Maryland unemployment rate is unadjusted.

In Maryland, there were 169,943 unemployed persons and 1.99 million jobholders in January, the state said.

The state said the December increase in unemployment could be attributed to seasonal layoffs in construction, food processing, apparel and textiles as well as a reduction in the state and local government workforce. Those unemployment increases were ameliorated to a degree by the regular seasonal hiring at retail stores.

In another development, the U.S. Labor Department announced that it has allocated $18.8 million to state governments to help retrain workers who have lost their jobs because of structural changes in the economy. The states have until March 1 to apply for Labor Department grants to operate a program to provide training, job search and relocation assistance to such workers. Depending upon the state's unemployment rate, jurisdictions will be required to match some percentage of the federal allotment.

The District is eligible for $68,863 and would have to provide $40,718. Maryland is eligible for $342,275 and would have to come up with an equal amount. Virginia is eligible for $282,792 and also would have to match the federal contribution.