Glutamate decarboxylase (GAD) can catalyze the decarboxylation of glutamate into γ-aminobutyrate (GABA) and is the only enzyme of GABA biosynthesis. Improving GAD activity and thermostability will be helpful for the highly efficient biosynthesis of GABA. According to the Ramachandran plot information of GAD 1407 three-dimensional structure from Lactobacillus brevis CGMCC No. 1306, we identified the unstable site K413 as the mutation target, constructed the mutant GAD by site-directed mutagenesis and measured the thermostability and activity of the wide type and mutant GAD. Mutant K413A led to a remarkably slower inactivation rate, and its half-life at 50 °C reached 105 min which was 2.1-fold higher than the wild type GAD1407. Moreover, mutant K413I exhibited 1.6-fold higher activity in comparison with the wide type GAD1407, although it had little improvement in thermostability of GAD. Ramachandran plot can be considered as a potential approach to increase GAD thermostability and activity.