A new algorithms for laser chaotic time series prediction was presented. The origin time series was decomposed as the measurement coefficients and wavelet coefficients based on the discrete stationary wavelet transform algorithms.The phase space of these coefficients was reconstructed by the theory of time delays. Based on the stability and the fractal of the chaotic attractor, the coefficients were predicted in their phase space. Finally the prediction of the coefficients were acquired by the inverse discrete stationary wavelet transform . The proposed algorithm was a better candidate for long range prediction.The simulation results prove the similarity of dynamic invariants between the origin and generated time series.And it shows that the proposed method can capture the dynamics of the nonlinear systems series effectively.