To enhance the approximation ability of neural networks, by introducing quantum rotation gates to the traditional BP networks, a novel quantum-inspired neural network model is proposed in this paper. In our model, the hidden layer consists of quantum neurons. Each quantum neuron carries a group of quantum rotation gates which are used to update the quantum weights. Both input and output layer are composed of the traditional neurons. By employing the error back propagation algorithm, the learning algorithms are designed. Simulation-based experiments using two application examples of pattern recognition and function approximation, respectively, illustrates the availability of the proposed model.