A new method is presented to investigate the globally asymptotic stability of reaction-diffusion cellular neural network with time-delays. The method is built on the mean Lyapunov function. We give some new sufficient conditions on time-dependent or time-independent to ensure globally asymptotic stability of the equilibrium point of the class of systems under the conditions of the active functions are continuous by employing linear matrix inequality (LMI). The results extend and improve the earlier works of other researchers. In additions, examples are given to show the application of the established stability theorems.