Abstract <p>We develop a fast method for solving non-autonomous anisotropic time-optimal control problem. The ordered upwind method (OUM) developed for the autonomous anisotropic time-optimal control problem can be extended to this non-autonomous case. OUM uses the search along the accepted front (SAAF) to update the value at considered nodes. Unfortunately, SAAF does significantly increase the computational cost in practice. To overcome this difficulty, neighbor-gradient single-pass method (NGSPM) without using SAAF is proposed for the autonomous control problem. Unfortunately, there are several difficulties in extending the NGSPM to the non-autonomous case. We propose a fast single-pass method for solving min-time non-autonomous anisotropic control problems by overcoming the difficulties of extending the NGSPM to the non-autonomous case. We show that our method is faster and more accurate than OUM via several numerical examples.</p>