We consider incoherent digital holography by two-step phase-shift method and phase-only correlation reconstruction. The two-step phase-shift method is a method of eliminating the bias term in the digital hologram by spatial frequency filtering. Compared with the four-step phase-shift method, reconstruction from a small number of interference fringe images is possible. By adopting the phase-only correlation reconstruction method, it is expected that a finer reconstructed image can be obtained as compared with a normal correlation reconstructed image. In this paper, we demonstrate that incoherent digital holography using these methods can be realized from experiments with a light emitting diode as light source.