Deep neural networks (DNNs) have demonstrated remarkable success in various fields. However, the large number of floating-point operations (FLOPs) in DNNs poses challenges for their deployment in resource-constrained applications, e.g., edge devices. To address the problem, pruning has been introduced to reduce the computational cost in executing DNNs. Previous pruning strategies are based on weight values, gradient values and activation outputs. Different from previous pruning solutions, in this paper, we propose a class-aware pruning technique to compress DNNs, which provides a novel perspective to reduce the computational cost of DNNs. In each iteration, the neural network training is modified to facilitate the class-aware pruning. Afterwards, the importance of filters with respect to the number of classes is evaluated. The filters that are only important for a few number of classes are removed. The neural network is then retrained to compensate for the incurred accuracy loss. The pruning iterations end until no filter can be removed anymore, indicating that the remaining filters are very important for many classes. This pruning technique outperforms previous pruning solutions in terms of accuracy, pruning ratio and the reduction of FLOPs. Experimental results confirm that this class-aware pruning technique can significantly reduce the number of weights and FLOPs, while maintaining a high inference accuracy.