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Model compression, such as pruning and quantization, has been widely applied to optimize neural networks on resource-limited classical devices. Recently, there are growing interest in variational quantum circuits (VQC), that is, a type of neural network on quantum computers (a.k.a., quantum neural networks). It is well known that the near-term quantum devices have high noise and limited resources (i.e., quantum bits, qubits); yet, how to compress quantum neural networks has not been thoroughly studied. One might think it is straightforward to apply the classical compression techniques to quantum scenarios. However, this paper reveals that there exist differences between the compression of quantum and classical neural networks. Based on our observations, we claim that the compilation/traspilation has to be involved in the compression process. On top of this, we propose the very first systematical framework, namely CompVQC, to compress quantum neural networks (QNNs).In CompVQC, the key component is a novel compression algorithm, which is based on the alternating direction method of multipliers (ADMM) approach. Experiments demonstrate the advantage of the CompVQC, reducing the circuit depth (almost over 2.5 %) with a negligible accuracy drop (<1%), which outperforms other competitors. Another promising truth is our CompVQC can indeed promote the robustness of the QNN on the near-term noisy quantum devices.