Based on the generalized empirical likelihood estimation method, a robust and effective estimation was proposed to realize the joint estimation of the mean and covariance matrix of longitudinal data in linear models. Using the Cholysky decomposition, the model was re-parameterized, and using the Lagrangian multiplier method, estimates were obtained, then, an estimate of the mean and covariance matrix was restored. Comparing the proposed method with other robust estimates in the literature in a simulation study, the results show that the proposed method is more efficient. Finally, the proposed method was used to analyze CD4 cell data. Cross-validation results show that the proposed method is more reliable.