Data augmentation is a widely adopted technique utilized to improve the robustness of automatic speech recognition (ASR). Employing a fixed data augmentation strategy for all training data is a common practice. However, it is important to note that there can be variations in factors such as background noise, speech rate, etc. among different samples within a single training batch. By using a fixed augmentation strategy, there is a risk that the model may reach a suboptimal state. In addition to the risks of employing a fixed augmentation strategy, the model's capabilities may differ across various training stages. To address these issues, this paper proposes the method of sample-adaptive data augmentation with progressive scheduling(PS-SapAug). The proposed method applies dynamic data augmentation in a two-stage training approach. It employs hybrid normalization to compute sample-specific augmentation parameters based on each sample's loss. Additionally, the probability of augmentation gradually increases throughout the training progression. Our method is evaluated on popular ASR benchmark datasets, including Aishell-1 and Librispeech-100h, achieving up to 8.13% WER reduction on LibriSpeech-100h test-clean, 6.23% on test-other, and 5.26% on AISHELL-1 test set, which demonstrate the efficacy of our approach enhancing performance and minimizing errors.