There are mainly two kinds of model for sample survey. These are model with fixed effects and model with mixed effects. The model with mixed effects contains fixed effects and random effects. Linear growth curve is one kind of mixed effect models. The growth curve which shows the growth rate against the time has many applications in science such as medicine, agriculture, economic and business. At first, linear growth curve model proposed by Rao (1959) for height and weight studying. In this thesis, we explain growth curve model. Then we do some parametric studies on this model. Finally, we will present some examples and theorem for more explains of the model.