Laser speckle spatial contrast analysis (LSSCA) is superior to laser speckle temporal contrast analysis (LSTCA) in monitoring the fast change in blood flow due to its advantage of high temporal resolution. However, the application of LSSCA which is based on spatial statistics may be limited when there is nonuniform intensity distribution such as fiber-transmitting laser speckle imaging. In this study, we present a normalized laser speckle spatial contrast analysis (nLSSCA) to correct the detrimental effects of nonuniform intensity distribution on the spatial statistics. Through numerical simulation and phantom experiments, it is found that just ten frames of dynamic laser speckle images are sufficient for nLSSCA to achieve effective correction. Furthermore, nLSSCA has higher temporal resolution than LSTCA to respond the change in velocity. LSSCA, LSTCA and nLSSCA are all applied in the fiber-transmitting laser speckle imaging system to analyze the change of cortical blood flow (CBF) during cortical spreading depression (CSD) in rat cortex respectively, and the results suggest that nLSSCA can examine the change of CBF more accurately. For these advantages, nLSSCA could be a potential tool for fiber-transmitting/endoscopic laser speckle imaging.