With the increasing requirement for resolution, the negligence of topography variations causes serious phase errors, which leads to the degradation of the focusing quality of the synthetic aperture (SAR) imagery, and geometric distortion. Hence, a precise and fast algorithm is necessary for high-resolution airborne SAR. In this paper, an extended back-projection (EBP) algorithm is proposed to compensate the phase errors caused by topography variations. Three-dimensional (3D) variation will be processed in the time-domain for high-resolution airborne SAR. Firstly, the quadratic phase error (QPE) brought by topography variations is analyzed in detail for high-resolution airborne SAR. Then, the key operation, a time-frequency rotation operation, is applied to decrease the samplings in the azimuth time-domain. Just like the time-frequency rotation of the conventional two-step approach, this key operation can compress data in an azimuth time-domain and it reduces the computational burden of the conventional back-projection algorithm, which is applied lastly in the time-domain processing. The results of the simulations validate that the proposed algorithm, including frequency-domain processing and time-domain processing can obtain good focusing performance. At the same time, it has strong practicability with a small amount of computation, compared with the conventional algorithm.