Convolutional Neural Networks(CNNs) are both computation and memory inten-sive which hindered their deployment in mobile devices. Inspired by the relevantconcept in neural science literature, we propose Synaptic Pruning: a data-drivenmethod to prune connections between input and output feature maps with a newlyproposed class of parameters called Synaptic Strength. Synaptic Strength is de-signed to capture the importance of a connection based on the amount of informa-tion it transports. Experiment results show the effectiveness of our approach. OnCIFAR-10, we prune connections for various CNN models with up to96%, whichresults in significant size reduction and computation saving. Further evaluation onImageNet demonstrates that synaptic pruning is able to discover efficient modelswhich is competitive to state-of-the-art compact CNNs such as MobileNet-V2andNasNet-Mobile. Our contribution is summarized as following: (1) We introduceSynaptic Strength, a new class of parameters for CNNs to indicate the importanceof each connections. (2) Our approach can prune various CNNs with high com-pression without compromising accuracy. (3) Further investigation shows, theproposed Synaptic Strength is a better indicator for kernel pruning compared withthe previous approach in both empirical result and theoretical analysis.