On the basis of analyzing the principles of the quantum rotation gates and quantum controlled-NOT gates, an improved design for CNOT gated quantum neural networks model is proposed and a smart algorithm for it is derived in our paper, based on the gradient descent algorithm. In the improved model, the input information is expressed by the qubits, which, as the control qubits after being rotated by the rotation gate, control the qubits in the hidden layer to reverse. The qubits in the hidden layer, as the control qubits after being rotated by the rotation gate, control the qubits in the output layer to reverse. The networks output is described by the probability amplitude of state |1> in the output layer. It has been shown in two application examples of pattern recognition and function approximation that the proposed model is superior to the standard error back-propagation networks with regard to their convergence rate, number of iterations, approximation ability, and robustness.