Super-resolution optical fluctuation imaging (SOFI) is an extensively used super-resolution (SR) imaging technique. The sample condition and imaging system are simpler than most SR systems, and the cusp-artifacts limit the resolution of high-order SOFI. To improve the resolution of SOFI, an alternative method is to improve the reconstruction algorithm. Here, compressive sensing (CS) is used in SOFI to improve its resolution. The detailed CS reconstruction algorithm is chosen as multiple measurement vector model sparse Bayesian learning (MSBL). We demonstrate that MSBL can achieve higher than threefold resolution improvement in simulation under certain conditions. The SOFI experiment analysis demonstrates that MSBL can improve the resolution about 2.5-fold compared with the diffraction limit. All results prove that MSBL has a higher resolving ability compared with other algorithms. Our results prove that CS is a broad applicability tool for most of the existing SR microscopy techniques and can be applied in 3D and live-cell SR fluorescence microscopy imaging in the future.