Abstract: The main purpose of this study is to investigate the performance of the Quarter-Sweep AOR (QSAOR) iterative method by using Caputo fractional derivative operator and implicit finite difference scheme to solve time-fractional diffusion equation. To solve the problems, a linear system will be constructed via discretization of the one-dimensional linear time-fractional diffusion equations by using the Caputo’s fractional derivative. Then the generated linear system has been solved using the proposed QSAOR iterative method. In the addition, the formulation and application of the QSAOR method to solve the problems are also presented. Two numerical examples and comparison with FSAOR and HSAOR methods are given to show the effectiveness of QSAOR method.