In this paper, a spectral collocation approach based on the sixth-kind Chebyshev polynomials (SKCPs) is constructed to solve a time-fractional stochastic diffusion equation (TFSDE). This method is applied to convert the solution of TFSDE to the solution of a system of nonlinear algebraic equations (NAEqs). Moreover, the convergence analysis of this suggested method is established. A numerical example is implemented to validate the efficiency of the proposed approach.