Combining the phase space reconstruction theory and the time series analysis theory, a prediction network applied to time series multi-step prediction is proposed. The network is constructed in the weight-sum form of some chaotic operators. Constant connections are adopted among the units. The control parameters of chaotic operators are adjusted by chaos optimization algorithm. The training samples, constructed by known time series data, are used in the training process only once, which makes the dynamic characteristics of the network change and tend to the predicted system with the lapse of time. The validity of the network can be proved by computing the Lyapunov exponent of prediction data. The multi-step predictions for engineering data are also realized by the method. Simulation results prove that the method could validly predict time series when the predictive step is not too long.