The proposed illuminator relates to white-light lamps based on LEDs with remote phosphor converters. The illuminator comprises a heat removing base with a radiation output opening, and the LEDs secured near the periphery of the opening, with, arranged in series at a distance from the LEDs, a concave phosphor converter layer, wherein the layer's concavity is oriented towards the LED's and the opening. White light formed as mix of reflected LED's radiation and phosphor's radiation exits via the opening, while white light formed as mix of LED's radiation passing through the layer and phosphor's radiation exits through the layer. The layer 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 opening, or a cylinder truncated by the plane of the opening.