In Deep Neural Network (DNN) accelerators, the on-chip traffic and memory traffic accounts for a relevant fraction of the inference latency and energy consumption. A major component of such traffic is due to the moving of the DNN model parameters from the main memory to the memory interface and from the latter to the processing elements (PEs) of the accelerator. In this paper, we present DNNZip, a technique aimed at compressing the model parameters of a DNN, thus resulting in significant energy and performance improvement. DNNZip implements a lossy compression whose compression ratio is tuned based on the maximum tolerated error on the model parameters provided by the user. DNNZip is assessed on several convolutional NNs and the trade-off inference energy saving vs. inference latency reduction vs. network accuracy degradation is discussed. We found that up to 64% energy saving, and up to 67% latency reduction can be obtained with a limited impact on the accuracy of the network.