Abstract: Growth curve model has broad application background, and plays an important role in some fields such as economics, biology, medical research. Many of existing estimation of its parameter matrix have been obtained based on the least squares method or maximum likelihood method. When distribution of the error term is partial peak, or heavy tail, or there exist outliers, estimation obtained by least square method will be invalid. The distribution of the error must be known in maximum likelihood estimation, which is often not satisfied. Quantile regression method can compensate for these defects and the estimation has good robustness. In this paper, quantile regression is used to give the estimation of growth curve model, and its asymptotic normality.