In this paper, we study the finite time stability of stochastic $\psi$-Hilfer fractional-order time-delay systems. Under the stochastic analysis techniques and the generalized Gronwall's inequality for $\psi$-fractional derivative, the criterion of finite time stability of the solution for nonlinear stochastic $\psi$-Hilfer fractional systems with time delay is obtained. An example is provided to illustrate the effectiveness of the proposed methods. Some known results in the literature are extended.