The trustees of the University of the District of Columbia, caught in the financial squeeze of the city's budget crisis, voted last night to double undergraduate tuition for D.C. residents next fall to $330 a year.

However, the board responded to strong complaints from the student government, and promised to hold a prublic hearing before the increase goes into effect.

Marjorie H. Parker, chairman of the board's finance committee, said the tuition increase was necessary because Mayor Marion Barry's planned budget for next year gives the university for less money than it needs. But she said the higher tuition along with improved college programs would have another salutory effect.

"We are often a university of last resort," Parker said, "but we are looking forward to [the time] when our main attraction will not be that we are the cheapest game in town."

Even so, UDC administrators distributed a chart showing that even with the increase, the college's tuition still probably would be the lowest in the area.

Although the finance committee originally proposed doubling the tuition rates for nonresidents and graduate students, as well as undergraduates, the board voted to increase all these rates by just the same amount -- $165 -- as the tuition for resident undergraduates. Thus undergraduate tuition for nonresidents will go up to $1,580, and the tuition for graduate students will be $777 for D.C. residents and $1,587 for nonresidents.

Parker said any larger increases for nonresidents and graduate students would be a self defeating because many students might leave UDC for older, more established universities, at which rates would be about the same.

One trustee, Daniel Fivel, proposed raising the rates for all non-U.S citizens to $2,000 a year, but Board Chairman Ronald H. Brown said the proposal might be unconstitutinal and it received no support from other members.

The plan said the reduction was necessary because of low enrollment in many departments and suggested that about 15 programs be eliminated. But it said most of the cutbacks probably could be carried out by hiring fewer part-time teachers.

The plan suggests major changes in the university's administrative structure, but no cutbacks in the number of nonfaculty positions -- a point that drew fire from several trustees last night.

In its resolution the board said it would hold public hearings on the plan and indicated it would probably make changes afterwards.