Convolution neural networks (CNNs) have shown great success in many areas such as object detection and pattern recognition. However, the high computational complexity of state-of-the-art deep CNNs makes them extreme difficult to be run on resource-constrained mobile and wearable devices. To address this design challenge, in this paper we first analyzed the filters' weights of pre-trained models from four state-of-the-art CNNs. We found that in all the CNNs that we analyzed, from about 20% (AlexNet) to 43% (VGG-19) of the weights are zeros, which lead to redundant large amounts of computation. Then, based on this observation, a zero-gating processing element (PE) design was proposed for low-power deep CNNs, in which the vast number of zeros in both activation maps and filter weights are explored to eliminate redundant computation for power reduction. We implemented our proposal with VGG-16 using ImageNet dataset. Experiments were conducted for evaluations of area and total power consumption. Compared with the baseline PE design without zero-gating, overall the proposed zero-gating PE can achieve 37% power saving while the corresponding area overhead is less than 8%.