Sunspot number time series, as a multivariable, strong coupling and nonlinear time series, has encountered troubles to describe its changes rules with modeling method owing to great complexity of sunspot number change. The main aim of this study is to develop a novel prediction method, based on the Quantum Neural Networks, which is composed of some quantum neurons and traditional neurons based on certain topology structure and connection rules. 308 years (1700-2007) actual Sunspot Number data are employed for developing prediction model, in which 258 years (1700-1957) are used for training Quantum Neural Networks (QNN) whilst 50 years (1958-2007) are used for testing the predictive ability of the model proposed. Through the comparison of its performance with the Common BP neural networks (CBPNN), it is demonstrated that the QNN model is a more effective method to predict the Sunspot Number time series.