The dark-line defect problem in the conventional polygon computer-generated hologram (CGH) is addressed. To resolve this problem, we clarify the physical origin of the defect and address the concept of phase-regularization. A novel synthesis algorithm for a phase-regularized polygon CGH for generating photorealistic defect-free holographic images is proposed. The optical reconstruction results of the phase-regularized polygon CGHs without the dark-line defects are presented.