Fractal characters and fractal dimension of time series created by repeller in complicated system were studied and the time series were reconstructed by applying the theory of phase space reconstruction for chaotic time series. The influence of zero-mean treatment, Fourier filter on prediction for time series were studied. The choice of prediction sample affects the relative error and the prediction length which were also under good concern. The results show that the model provided here are practical for the modeling and prediction of time series created by chaotic repellers. Zero-mean treatment has changed prediction result quantitatively for chaotic repeller sample data. But using Fourier filter may decrease the prediction precision. This is theoretical and practical for study on chaotic repeller in complicated system.