We propose a parallel phase-shifting digital holography as a technique capable of noiseless instantaneous applications for three-dimensional objects such as measurement and object recognition. The technique carries out the three-step-phase-shifting at a time using a phase-shifting array device located in the reference beam. The device is an array of three kinds of phase retarders. We numerically simulate the reconstructed image by the technique. The result of the simulation agrees well with that of the conventional phase-shifting digital holography, and it is superior to the result obtained by the conventional digital holography using a Fresnel transform alone, which is another technique capable of instantaneous applications.