Score test statistic has been successfully used to solve many problems in the regression model.In this paper,we use the method to study the problem of local influence of a covariance perturbation in a growth curve model. First, we establish the score test function of the growth curve model with a variance enlargement under Rao's Simple Structure (Abbr.: RSS).Second, we discuss similar problems of the model with a general covariance structure (Abbr.: GCS). Furthermore, we give an approach to detecting one outlier or some outliers. The numerical example analysed at the end shows that our results are very useful in practice.