Cross-over designs have been widely used in clinical trials to investigate the efficacy of new treatments. In cross-over design, each subject is treated subsequently with different treatments. Many methods such as linear mixed models (LMMs) and generalized estimating equation (GEE) models have been used to analyze the repeated measurements from cross-over design. When we consider repeated measured response variables, estimation of random components for LMMs is not always easy. In this article, we applied the GEE method to cross-over design to overcome the limitation of LMMs. To apply the GEE model to the data from the cross-over designs, we need to switch the role of variables in LMM such a way that the independent variable in LMMs is considered as a response variable in GEE model and vice versa. The purpose of this study is to compare the performance of these GEE models and LMMs for cross-over designs. Through simulation studies, we checked the type I errors and compared power to evaluate the performance of the proposed GEE model and LMMs.