This study is designed to fit the term structure of Taiwan government bond market by applying the cubic exponential spline method on ev.ery Wednesdays from 1995/6/2 1 to 1999/12/29. It is presumed in the study that the functional form of discount factor is a cubic exponential spline function. Since the estimated parameters are used to calculate the discount function for each period, the term structure of interest rates can then be obtained through the discount function. In this sense, the linear and nonlinear optimization methods are employed respectively to estimate parameters embedded in the discount function. The result of this study shows that, with the application of linear optimization method, the fitting errors is smaller and fitting time is shorter than those estimated by nonlinear optimization method Therefore, with the concern of reducing the fitting error and the fitting time, the linear optimization approach is a better fitting method than nonlinear optimization method.