Memristive devices are building blocks for neuromorphic computing. However, non‐ideal properties of memristive devices, such as bad retention, small number of resistance states, and nonlinear pulse programming hinder the development of neuromorphic computation. Based on proton migration in the α‐MoO3/SrCoO2.5 stack, a Pt/α‐MoO3/SrCoO2.5/Nb‐SrTiO3 memristive device is developed with multiple resistance states and excellent nonvolatility. When protons migrate from α‐MoO3 to the SrCoO2.5 lattice, both layers undergo a resistance increase, due to a reduced doping level in α‐MoO3 along with the loss of protons, and a larger direct bandgap of SrCoO2.5 resulted from the insertion of protons. While protons migrate from SrCoO2.5 to α‐MoO3, the device resistance decreases, because of the increased proton concentration in α‐MoO3 and the decreased proton concentration in the SrCoO2.5 layer. The device also realizes nearly linear potentiation and depression under appropriate pulse schemes. A three‐layer backpropagation neural network constructed with the memristive devices acquires an accuracy of 94.3% for the recognition of MNIST handwritten digits.