Structured illumination microscopy (SIM) has been widely applied to investigate intricate biological dynamics due to its outstanding super-resolution imaging speed. Incorporating compressive sensing into SIM brings the possibility to further improve the super-resolution imaging speed. Nevertheless, the recovery of the super-resolution information from the compressed measurement remains challenging in experiments. Here, we report structured illumination microscopy with complementary encoding-based compressive imaging (CECI-SIM) to realize faster super-resolution imaging. Compared to the nine measurements to obtain a super-resolution image in a conventional SIM, CECI-SIM can achieve a super-resolution image by three measurements; therefore, a threefold improvement in the imaging speed can be achieved. This faster imaging ability in CECI-SIM is experimentally verified by observing tubulin and actin in mouse embryonic fibroblast cells. This work provides a feasible solution for high-speed super-resolution imaging, which would bring significant applications in biomedical research.