All-inorganic perovskite CsPbX3 (X = Cl, Br, or I) is widely used in a variety of photoelectric devices such as solar cells, light-emitting diodes, lasers, and photodetectors. However, studies to understand the flexible CsPbX3 electrical application are relatively scarce, mainly due to the limitations of the low-temperature fabricating process. In this study, all-inorganic perovskite CsPbBr3 films were successfully fabricated at 75 °C through a two-step method. The highly crystallized films were first employed as a resistive switching layer in the Al/CsPbBr3/PEDOT:PSS/ITO/PET structure for flexible nonvolatile memory application. The resistive switching operations and endurance performance demonstrated the as-prepared flexible resistive random access memory devices possess reproducible and reliable memory characteristics. Electrical reliability and mechanical stability of the nonvolatile device were further tested by the robust current-voltage curves under different bending angles and consecutive flexing cycles. Moreover, a model of the formation and rupture of filaments through the CsPbBr3 layer was proposed to explain the resistive switching effect. It is believed that this study will offer a new setting to understand and design all-inorganic perovskite materials for future stable flexible electronic devices.