To analyze and simulate non-stationary time series with finite length, the statistical characteristics and auto-regressive (AR) models of non-stationary time series with finite length are discussed and studied. A new AR model called the time varying parameter AR model is proposed for solution of non-stationary time series with finite length. The auto-covariances of time series simulated by means of several AR models are analyzed. The result shows that the new AR model can be used to simulate and generate a new time series with the auto-covariance same as the original time series. The size curves of cocoon filaments regarded as non-stationary time series with finite length are experimentally simulated. The simulation results are significantly better than those obtained so far, and illustrate the availability of the time varying parameter AR model. The results are useful for analyzing and simulating non-stationary time series with finite length.