Holographic head-mounted display (HHMD) is a specific application of holography. The previous conventional computer-generated hologram (CGH) generation method has a large redundancy and suffers from a heavy computing burden in the HHMD. A low redundancy and fast calculation method is presented for a CGH that is suitable for an HHMD with the effective diffraction area recording method. For the limited pupil size of an observing eye, the size of the area producing an effective wavefront is very small, and the calculated amount can be dramatically reduced. A numerical simulation and an augmented virtual reality experimental system are presented to verify the proposed method. 1.5% of the calculation consumption of the conventional CGH generation method is used, and good holographically reconstructed images can be observed.