The proposed illuminator relates to white-light lamps based on LEDs with remote photoluminescent converters. The illuminator comprises a heat removing base with a radiation output orifice, and the LEDs secured near the periphery of the orifice, with, arranged in series at a distance from the a concave photoluminescent converter layer and a concave light reflector, wherein the converter layer's and light reflector's concavities are oriented towards the LED's and the opening. White light mix of the LEDs' and converter layer's radiation exits via the orifice. The converter layer and reflector may have the form of a truncated ellipsoid of revolution, in particular a sphere, or a paraboloid, with a main axis perpendicular to the plane of the orifice, or a cylinder truncated by the plane of the orifice. The outside reflector' surface may have ribbed heat radiators associated with the heat removing base.