In this paper, a modified residual fractional power series technique is applied to provide an analytic-numeric approximated solution for linear time-fractional Swift-Hohenberg equation. The proposed algorithm relies on minimizing the residual error that results when approximating the solution by a truncated fractional Taylor series. The fractional derivative is computed by Caputo time-fractional derivative. The approximate solution obtained by the proposed approach is coinciding well with the exact one. To test the potentially, accuracy and reliability of the proposed technique, the linear time-fractional Swift-Hohenberg equation is considered. The numerical results indicate that the residual fractional power series method is simple, accurate, efficient and suitable for solving various types of differential equations with fractional order.