Abstract: Growth curve model is a general multivariable linear model. It plays an important role in modern statistics. In this paper, firstly, we define the penalized least squares for growth curve model, after transforming it by the Potthoff-Roy transformation. By using adaptive LASSO we can get corresponding estimation, as well as achieve the variable selection. Then, the penalized least squares estimation of the growth curve model is presented with a unified expression of approximate estimation. In addition, we discuss the properties of the penalized least squares estimations of the growth curve model, which is transformed by Potthoff-Roy transformation, and the properties, which are Oracle properties, are proved in this paper. By using the criteria to measure estimation and variable selection, we compare several penalized least squares estimations and the effect of variable selection of different penalty functions. The result shows that the adaptive LASSO performs better in parameter estimation and variable selection. Besides, we compare different transformations. Results indicate that Potthoff-Roy transformation performs better than matrix stacking transformation when considering variable selection and parameter estimation comprehensively.