The structure, mobility and memristor properties of tetragonal CH3NH3PbBr3 single crystals (T-MAPbBr3 SC) are rarely reported. In this study, we synthesized T-MAPbBr3 SC with the P4/mmm (123) space group by the growing, dropping and growing (GDG) crystal seed method. A CH3NH3+ cation is a disordered state in T-MAPbBr3 SC. The mobility values of T-MAPbBr3 SC under light and dark conditions are 464.28 and -1685.3 cm2 V-1 s-1, respectively. The carrier types under light and dark conditions are holes and electrons, respectively. The memristor based on T-MAPbBr3 SC has a wide and low operating voltage window (0-0.9 V). The high and low resistances of the memristor based on T-MAPbBr3 SC achieve values of 41 and 0.35 GΩ, respectively. The values of high and low resistances are relatively stable for 100 cycles. Thus, the memristor device based on T-MAPbBr3 SC has good applications in the field of memristors.