Organic-inorganic halide perovskite materials exhibit excellent memristive properties, such as a high on/off ratio and low switching voltage. However, most studies have focused on Pb-based perovskites. Here, we report on the resistive switching and neuromorphic computing properties of Pb-free perovskite-related MA3Sb2Br9 (MA = CH3NH3). The Ag/PMMA/MA3Sb2Br9/ITO devices show forming-free characteristics due to a self-formed conducting filament induced by metallic Sb present in the as-prepared MA3Sb2Br9 layer. An MA3Sb2Br9-based memristor exhibits a reliable on/off ratio (∼102), an endurance of 300 cycles, a retention time of ∼104 s and multilevel storage characteristics. Furthermore, synaptic characteristics, such as short-term potentiation, short-term depression and long-term potentiation, are revealed along with a low energy-consumption of 117.9 fJ μm-2, which indicates that MA3Sb2Br9 is a promising material for neuromorphic computing.