Mixed-effect models are often applied to data analysis in various fields because they enable us to incorporate potential differences among individuals as random effects. Although the random effect is often assumed to follow a normal distribution, a validity evaluation of this assumption is difficult because the random effect is not observed. Therefore, it is concerned that if the assumption of normality for random effect is invalid, estimates derived from the mixed-effect model would have bias and instability. To check the validity of assumption for random effect distribution, Efendi et al. (2014) proposed a test based on the bootstrap sampling, and evaluated its performance via simulation under the null hypothesis that random effect follows a normal distribution. The simulation result shows the power is low when the true distribution is symmetric normal mixture. We proposed alternative test statistic which modified Efendi's one in linear mixed model, finding our test has higher power in the above situation. In this study, we will extend our test to generalized linear mixed models, and evaluate the performance of the proposed method and compare with Efendi's one by simulation.