This paper investigates the stochastic stability of fuzzy neural networks with Markovian jumping parameters and mixed delays under impulsive per- turbations in mean square. The mixed delays consist of time-varying delay and continuously distributed delay. By employing a new Lyapunov-Krasovskii functional, linear convex combination technique, a novel reciprocal convex lemma and the free-weight matrix method, two novel sufficient conditions are derived to ensure the stochastic asymptotic stability of the equilibrium point of the considered networks in mean square. The proposed results, which are expressed in terms of linear matrix inequalities, can be easily checked via Matlab LMI Toolbox. Finally, two numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over existing literature.