In this paper, a quantum extension of classical deep neural network (DNN) is introduced, which is called QDNN and consists of quantum structured layers. It is proved that the QDNN can uniformly approximate any continuous function and has more representation power than the classical DNN. Moreover, the QDNN still keeps the advantages of the classical DNN such as the non-linear activation, the multi-layer structure, and the efficient backpropagation training algorithm. Furthermore, the QDNN uses parameterized quantum circuits (PQCs) as the basic building blocks and hence can be used on near-term noisy intermediate-scale quantum (NISQ) processors. A numerical experiment for an image classification task based on QDNN is given, where a high accuracy rate is achieved.