We examine the evolution of a Hoyle-Lyttleton accretor, on which mass accretion takes place via the Hoyle-Lyttleton processes, while taking into account the luminosity of the accretor. We consider two cases: (i) a spherical accretor, where the accretor is a spherical radiating source, and (ii) a disk accretor, where the accretor is a disk radiating source. In the well-known case of the classical non-luminous accretor, the growth time depends on the mass, the gas density, and the relative velocity, although the evolution processes are enhanced due to dynamical friction; the evolution time is shortened roughly by a factor of the Coulomb logarithm. In the case of a luminous accretor, we found, the evolutionary picture is drastically changed. The mass of the spherical accretor grows exponentially, but the luminosity approaches the Eddington luminosity, where the evolution timescale is the Eddington timescale, £E (= 4.53 x 10 8 ?7 yr, r\ being the efficiency). The mass and the effective luminosity of the disk accretor, on the other hand, diverge to infinity within a finite time, which is shorter than the Eddington timescale by a factor of the Coulomb logarithm. We discuss applications to several astrophysical situations, including a slow mover in giant molecular clouds and a fast runner in Thorne-Zytkow objects.