Hand gesture recognition has long been a hot topic in human computer interaction. Traditional camera-based hand gesture recognition systems cannot work properly under dark circumstances. In this paper, a Doppler Radar based hand gesture recognition system using convolutional neural networks is proposed. A cost-effective Doppler radar sensor with dual receiving channels at 5.8GHz is used to acquire a big database of four standard gestures. The received hand gesture signals are then processed with time-frequency analysis. Convolutional neural networks are used to classify different gestures. Experimental results verify the effectiveness of the system with an accuracy of 98%. Besides, related factors such as recognition distance and gesture scale are investigated.