A compressor for a gas turbine engine having a bleed air recirculation system includes a plurality of bleed holes extending through the shroud at a first axial location thereon substantially adjacent the blade tips. The bleed holes have a closed outer perimeter along their complete length. An annular bleed cavity surrounds the shroud and is in communication with outlet openings of the bleed holes. The bleed holes provide communication between the main gas flow passage and the bleed cavity. The bleed cavity includes exit passages having outlets disposed in the shroud at a second axial location which is upstream of both the first axial location and the leading edge of the blades of the rotor. Bleed air is passively bled from the main gas flow passage via the bleed holes, recirculated through the bleed cavity and re-injected back into the main gas flow passage at the second axial location.