Linear mixed effects models provide a powerful tool for analyzing grouped data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed effects models with high-dimensional fixed effects. The propose method is applicable to general settings where the group sizes are possibly large or unbalanced and the designs for fixed effects and random effects are possibly correlated. Regarding the fixed effects, we provide rate optimal estimators and valid inference procedures which are free of the assumptions on the specific structure of the variance components. Separately, rate optimal estimators of variance components are derived under mild conditions. We prove that, under proper conditions, the convergence rate for estimating the variance components of random effects does not depend on the accuracy of fixed effect estimation. Computationally, the proposed method is loop-free and convex. The proposed method is assessed in various simulation settings and is applied to a real study regarding the associations between the body weight index and polymorphic markers in a stock mice population.