Most of the current speech data augmentation methods operate on either the raw waveform or the amplitude spectrum of speech. In this paper, we propose a novel speech data augmentation method called PhasePerturbation that operates dynamically on the phase spectrum of speech. Instead of statically rotating a phase by a constant degree, PhasePerturbation utilizes three dynamic phase spectrum operations, i.e., a randomization operation, a frequency masking operation, and a temporal masking operation, to enhance the diversity of speech data. We conduct experiments on wav2vec2.0 pre-trained ASR models by fine-tuning them with the PhasePerturbation augmented TIMIT corpus. The experimental results demonstrate 10.9\% relative reduction in the word error rate (WER) compared with the baseline model fine-tuned without any augmentation operation. Furthermore, the proposed method achieves additional improvements (12.9\% and 15.9\%) in WER by complementing the Vocal Tract Length Perturbation (VTLP) and the SpecAug, which are both amplitude spectrum-based augmentation methods. The results highlight the capability of PhasePerturbation to improve the current amplitude spectrum-based augmentation methods.