Abstract: In this paper, we consider the following semiparametric regression model for longitudinal data: y_ij=x_ij'\beta+g(t_ij)+e_ij. The estimators of \beta and g(\cdot) are obtained by using the least squares and usual nonparametric weight function method, the asymptotic normality of the estimator of \beta and the optimal convergence rate of the estimator of g(\cdot) are proved under the suitable conditions. Some simulations are conducted to demonstrate the finite sample performances of the estimation procedures.