The stability problem of T-S fuzzy systems with random time-varying delay is investigated in this article. First, a new random variable dependent system model is established by considering the stochastic time-varying characteristics of time-varying delay, and the original systems can be implied by it. Based on the new system model, a suitable Lyapunov functional is constructed that can utilize the information of membership function, random time-varying delay and its derivative. The fuzzy reciprocally convex integral inequality is used to estimate the quadratic integral term from the derivative of the Lyapunov functional, and a new membership function and derivative of delay function dependent system stability criterion is proposed. For both known and unknown cases of system random time-varying delay function, the obtained stability criterion is applicable, and has less conservatism. Finally, the effectiveness of the proposed stability criterion is verified through two numerical examples.