Summary: This paper is concerned with global asymptotic stability of a class of reaction-diffusion stochastic bi-directional associative memory (BAM) neural networks with discrete and distributed delays. Based on suitable assumptions, we apply the linear matrix inequality method to propose some new sufficient stability conditions for reaction-diffusion stochastic BAM neural networks with discrete and distributed delays. The obtained results are easy to check and improve upon the existing stability results. An example is also given to demonstrate the effectiveness of the obtained results.