In this paper, an operational matrix approach based on hybrid of block-pulse and parabolic functions (HBPFs) has been introduced for solving a modern class of stochastic differential equations (SDEs). The mechanism of this approach is based on stochastic and fractional integration operational matrices, which transform the intended problem to a nonlinear system of algebraic equations. Thus, the complexity of solving the mentioned problem is reduced significantly. Finally, the accuracy and efficiency of the proposed algorithm have been experimentally investigated through a test problem.