The global asymptotic stability problem for a class of reaction-diffusion Cohen-Grossberg neural networks with both time-varying delay and infinitely distributed delay is investigated under Dirichlet boundary conditions. Instead of using the M-matrix method and the algebraic inequality method, under some suitable assumptions and using a matrix decomposition method, we adopt the linear matrix inequality method to propose two sufficient stability conditions for the concerned neural networks with Dirichlet boundary conditions and different kinds of activation functions, respectively. The obtained results are easy to check and improve upon the existing stability results. Two examples are given to demonstrate the effectiveness of the obtained results.