Several methods for predicting random effects in linear mixed effects models have been proposed. The performances of these methods have not been thoroughly investigated when the normality assumption for the random effects is violated, except for the empirical Bayes (EB) approach, as well as comparisons of the methods. This study compared the prediction accuracy of the EB approach with that of an approach based on quadratic inference functions (QIFs) under different distributional assumptions for the random effects, using a longitudinal linear model that included a random intercept and a random slope for time. The simulations revealed that the EB approach was generally superior to the QIF approach in predicting the random effects, even under non-normal distributions for the random effects, except in some scenarios with very large error variances. In addition, the EB approach is mathematically and computationally less complex. Thus, our study suggests that the EB approach is more recommendable as the first choice in statistical practice, even if non-normal random effects are suspected. An application to the prediction of individual benefits of an anti-depressan drug was considered.