Super-resolution localization microscopy (SRLM) breaks the diffraction limit, making possible the observation of sub-cellular structures. Challenges remain in SRLM due to a long data acquisition time. To overcome the limitation, the methods based on compressed sensing (CS) have been proposed. However, at the current stage, the widely used sparsity-based localization methods, e.g., interior point method (IPM), is computationally intensive. To address the problem, in this paper, we introduce an alternative CS reconstruction method to super-resolution imaging model, which is achieved by using gOMP (generalized Orthogonal Matching Pursuit). A series of numerical simulations with varying emitter densities and signal-to-noise rations (SNRs) are performed to evaluate the performance of gOMP method. The results show that whatever gOMP or IPM is used in SRLM, the obtained localization accuracy is similar. But, the data-processing time of gOMP can be significantly reduced (< 100 times) than the previous reported IPM method. As a result, gOMP provides the potential for reducing the computational cost while maintaining a desired spatial resolution, which is beneficial for SRLM imaging.