Abstract: Inspired by the principle of superposing states in quantum mechanics, a new kind of feedforward neural network with single hidden layer was designed and named as Quantum Neural Networks. It has mainly been used for data classification. Multilevel activation functions is adopted in Quantum Neural Networks and a different objective function is used for the learning of quantum intervals of the multilevel hidden units: minimizing the class-conditional variances at the outputs of the hidden units. Quantum Neural Networks is endowed with a special ability of identifying uncertainty in data classification by its unique design. However, as different objective functions are used for the learning of synaptic weights and quantum intervals, conflict is observed in the iterative training process which will cause more iteration times for training and degrades the training results. Using the theory of Constrained Optimization, a new training algorithm is proposed in this paper by introducing penalty function into the steepest descent method. In the new training algorithm, the conflict is removed. Experimental results indicate that the new algorithm can increase the training speed and improve the performance of the trained network remarkably.