Convolutional neural network (CNN) is an indispensable building block for designing a state of the art system for acoustic event classification (AEC). By stacking multiple CNN layers, the model could explore long-range dependency of explored features in top layers with increasing of feature abstraction. However it is also possible that the discriminative features with short-range dependency which are distributed locally are smooth out in the final representation. In this paper, we propose a progressive multi-scale attention (MSA) model which explicitly integrates multi-scale features with short-and longrange dependency in feature extraction. Based on mathematic formulations, we revealed that the conventional residual CNN (ResCNN) model could be explained as a special case of the proposed MSA model, and the MSA model could use the ResCNN as a backbone with an attentive feature weighting in consecutive scales. The discriminative features in multi-scales are progressively propagated to top layers for the final representation. Therefore, the final representation encodes multi-scale features with local and global discriminative structures which are expected to improve the performance. We tested the proposed model on two AEC data corpora, one is for urban acoustic event classification task, the other is for acoustic event detection in smart car environments. Our results showed that the proposed MSA model effectively improved the performance on the current state-of-the-art deep learning algorithms.