Abstract: This paper studies the quantum theory and the principle of Quantum Neural Network (QNN). Model of Quantum Forward Counter Propagation Neural Network (QFCPNN) and Recursive?Weighted Least Squares Quantum Forward Counter Propagation Algorithm (RWLS_QFCPA) are analyzed. Definition and knowledge set of QFCPNN is proposed. Adaptive Quantum Forward Counter Propagation Algorithm (AQFCPA) is proposed and its convergence is proved. Full account of overall situations of learning rates before current learning, this algorithm improves network convergence by adaptively changing the learning rate and controls timely changing learning rate. This new algorithm effectively overcomes some defects including network oscillations divergence due to high learning rate and reducing network convergence speed due to low learning rate. The simulation results indicate that AQFCPA has less number of iterations of network training and higher classification accuracy relative to RWLS_QFCPA.