The presence of non-speech segments in utterances often leads to the performance degradation of speaker verification. Existing systems usually use voice activation detection as a preprocessing step to cut off long silence segments. However, short silence segments, particularly those between speech segments, still remain a problem for speaker verification. To address this issue, in this paper, we propose a simple wave-level data augmentation method, \textit{PadAug}, which aims to enhance the system's robustness to silence segments. The core idea of \textit{PadAug} is to concatenate silence segments with speech segments at the waveform level for model training. Due to its simplicity, it can be directly applied to the current state-of-the art architectures. Experimental results demonstrate the effectiveness of the proposed \textit{PadAug}. For example, applying \textit{PadAug} to ResNet34 achieves a relative equal error rate reduction of 5.0\% on the voxceleb dataset. Moreover, the \textit{PadAug} based systems are robust to different lengths and proportions of silence segments in the test data.