Charles Draper, the District's public housing director since November, has submitted his resignation, the second straight public housing chief to leave the job after serving less than a year.

Draper, 42, submitted his resignation from the $56,164-a-year position last Friday, effective July 18, but gave no reason, according to Madeline M. Petty, director of the D.C. Department of Housing and Community Development. Draper declined to comment yesterday.

Petty said she will conduct a nationwide search for a new public housing director and hopes to fill the job within 90 days. In the meantime, Petty said that Jo Fisher-Hall, Draper's chief assistant, would be the acting public housing director, overseeing management of the city's 12,000 public housing units where about 60,000 people live.

The city's public housing program has been plagued with a long list of problems in recent years, including serious delinquencies in collecting rents and major deterioration of hundreds of units. Petty, while acknowledging "there are no overnight quick fixes," said she is "optimistic we'll have numerous candidates" to head the public housing department.

Petty said that in the last 1 1/2 years the housing department has collected nearly $1.8 million in overdue rents, leaving $2 million in additional delinquencies. She said that after an audit is completed, some of the remaining delinquencies will be written off and attempts made to collect the remainder.

In addition, she said that within two years, a large-scale renovation and modernization of about 3,600 units will be completed.

Prior to Draper, the city's public housing program was headed by Donald L. Harris, who resigned in April 1984 after serving seven months. He cited personal reasons for leaving, but shortly before his resignation he had been placed on administrative leave for two days after a heated argument with James E. Clay, the housing department's former director.