The building, at 83-67 116th St., between Curzon Road and 84th Avenue, would replace a large 2-story home.
There would be storage and laundry rooms in the basement, the lobby and three apartment units on the first floor would, and five to seven units per story on the remaining floors, according to the application.
The building would have no commercial space.
The application, filed earlier this week by Whitestone-based Curzon Development LLC, is currently pending.
The developer, who did not immediately respond to a phone call seeking comment, is also planning to build another residential building around the corner. That building, at 116-22 Curzon Road, would be 6-stories high and would feature 17 apartments with no on-site parking.
The quiet and leafy neighborhood known for its mansion-like houses and a large number of co-ops, has recently been attracting the attention of developers who built several new condominiums in the area in recent years.