A high-power multi-transverse modes random fiber laser (RFL) is investigated by combining a master oscillator power-amplifier (MOPA) configuration with a segment of extra-large mode area step-index multimode fiber (MMF). Spatial coherence of the high-power multi-transverse modes RFL has been analyzed, which shows that speckle contrast is reduced dramatically with the output power increasing. In this way, considerably low speckle contrast of ~0.01 is achieved under high laser power of ~56 W, which are the records for multi-transverse modes RFLs in both spatial coherence and output power. This work paves a way to develop high-power RFLs with very low spatial coherence for wide-range speckle-free imaging and free-space communication applications.