In this paper, an inverse problem of determining an unknown source term in a time-fractional diffusion equation is investigated. This inverse problem is severely ill-posed. For this reason, a mollification technique is used to obtain a regularized problem. Afterwards, a finite difference marching scheme is introduced to solve this regul arized problem. The stability of numerical solution are investigated. Finally, two numerical examples are presented to illustrate the validity an d effectiveness of the proposed method.