This paper is concerned with mean square exponential stability of switched stochastic system with interval time‐varying delays. The time delay is any continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a suitable augmented Lyapunov‐Krasovskii functional combined with Leibniz‐Newton’s formula, a switching rule for the mean square exponential stability of switched stochastic system with interval time‐varying delays and new delay‐dependent sufficient conditions for the mean square exponential stability of the switched stochastic system are first established in terms of LMIs. Numerical example is given to show the effectiveness of the obtained result.