Abstract: In the research it is frequently assumed that the growth curve is a polynomial in time. In practice, researchers mainly use higher-order polynomials to obtain more precise estimates. But this method has many defects, such as the model can be easily affected by outliers and the polynomial hypothesis may be much strong in practice. So in this paper we first proposed nonparametric approach, local polynomial, instead of parametric method for estimation in growth curve model. We give the nonparametric growth curve model, and its nonparametric estimation. Then discuss the large sample character of local polynomial estimate. The ideal theoretical choice of a local bandwidth is also discussed in detail in this paper. Finally, through the simulation study, from the fitting curve and average square error box plot we can clearly see that the performance of nonparametric approach is much better than parametric technique.