We investigate Hoyle-Lyttleton accretion for the case where the central source is a luminous accretion disk. In Hoyle-Lyttleton accretion onto a “spherical” source, accretion takes place in an axially symmetric manner around a so-called accretion axis and the accretion rate Ṁ is given as ṀHL(1 − Γ)2, where ṀHL is the accretion rate of the classical Hoyle-Lyttleton accretion and Γ is the central luminosity normalized by the Eddington one. If the central object is a compact star with a luminous accretion disk, the radiation field becomes “non-spherical”. In such a case the axial symmetry around the accretion axis breaks down and the accretion rate Ṁ depends on an inclination angle i between the accretion axis and the symmetry axis of the disk. In the case of pole-on accretion (i = 0) the accretion rate becomes smaller than that of the spherical case. We found that the accretion rate is approximately expressed as dot Ṁ ∼ ṀHL(1− Γ)(1 − 2Γ). In the case of edge-on accretion (i = 90°) the shape of the accretion cross-section varies from a circle (Γ = 0), an ellipse, a hollow ellipse (Γ ∼ 0.5), and a twin lobe (Γ ≳ 0.65). The accretion rate is larger than that of the spherical case, and approximately expressed as Ṁ ∼ ṀHL(1 − Γ) for Γ ≤ 0.65 and Ṁ ∼ ṀHL(2 − Γ)2/5 for Γ ≥ 0.65. Once the accretion disk forms and the anisotropic radiation fields are produced around the central object, the accretion plane (and the direction of jets) will be maintained automatically. Thus, the anisotropic radiation field of accretion disks drastically changes the accretion nature, which gives a clue to the formation of accretion disks around an isolated black hole. Hoyle-Lyttleton type accretion onto the accretion disk may take place in various astrophysical situations, including the galactic center X-ray source 1E 1740.7–2942.