The paper considers the parallel algorithm for solving the inverse problem of identifying the space-dependent right-hand part of a time-fractional diffusion equation. After discretization and approximation, the initial boundary problem is reduced to solving the systems of linear algebraic equations. For solving the inverse problem, the iterative conjugate gradient method is used. It requires solving the auxilliary initial boundary problem at each iterative step. On the basis of the parallel sweep method, a parallel algorithm is implemented for multicore processors. Numerical experiments were performed.