Rockville City Manager Richard V. Robinson has proposed a $37.7 million, six-year capital improvements budget for the city for the fiscal year starting in July.

Because several major construction projects have been completed, next year's proposal is about $300,000 smaller than the current year's spending plan, he said.

The budget will be discussed at public hearings next Tuesday and May 27 at Rockville City Hall. The council and mayor will vote on it in the first week of June.

James M. Davis, Rockville planning director, said $21 million is earmarked for transportation projects, down from $20 million in last year's budget.

Davis said the slight cut in the overall budget was possible because the city recently completed several substantial projects, such as the Gude Drive Bridge over I-270, and the extensions of Research Boulevard and First Street.

Among the proposed major transportation expenditures, Davis said, is continued construction of Ritchie Parkway, a $14 million project begun two years ago, which will cost the city $2.5 million in fiscal year 1987, and $2.7 million for the design plans for West Montgomery Avenue. Davis said the budget also proposes spending $250,000 on improvements to the F. Scott Fitzgerald Theater, matching the amount set aside by the Maryland Legislature this session for the project.