In the super-resolution microscopy imaging technology, single molecule localization microscopy is one of the widely used techniques. In this paper, in order to achieve super-resolution fluorescence image reconstruction, a multiple measurement vector Compressed sensing (MMV-CS) model was established based on the principle of fluorescence microscopic imaging, and the multiple sparse Bayesian learning algorithm was applied in problem solving. The effects of the effective pixel size, the number of photons generated by fluorescent molecules and the Poisson noise of fluorescence and background signal on the reconstruction results were analyzed. The running time of the algorithm was analyzed with the image subdivided into smaller patches. The results of simulation and experimental calculation show that when the standard deviation of the point spread function is 160 nm, the effective pixel size at 120 nm, 160 nm and 200 nm can achieve good reconstruction effect, while the pixel size at 60 nm results in poor effect. Better reconstruction image quality is achieved with more photons collected by the detector. As the background signal photons increase, the sample structure becomes indistinguishable when the distance is too close. Under the same subdivided condition, MMV-CS is one order of magnitude faster than the Homotopy (L1-H) algorithm and three orders of magnitude faster than the convex optimization algorithm (CVX), which has greater advantages in terms of running time for the application of MMV-CS in 3D super-resolution fluorescence microscopy.