SrFeO _x(SFO) is a kind of material that can undergo a reversible topotactic phase transformation between an SrFeO _2.5brownmillerite (BM) phase and an SrFeO ₃perovskite (PV) phase. This phase transformation can cause drastic changes in physical properties such as electrical conductivity, while maintaining the lattice framework. This makes SFO a stable and reliable resistive switching (RS) material, which has many applications in fields like RS memory, logic operation and neuromorphic computing. Currently, in most of SFO-based memristors, a single BM-SFO layer is used as an RS functional layer, and the working principle is the electric field-induced formation and rupture of PV-SFO conductive filaments (CFs) in the BM-SFO matrix. Such devices typically exhibit abrupt RS behavior, i.e. an abrupt switching between high resistance state and low resistance state. Therefore, the application of these devices is limited to the binary information storage. For the emerging applications like neuromorphic computing, the BM-SFO single-layer memristors still face problems such as a small number of resistance states, large resistance fluctuation, and high nonlinearity under pulse writing. To solve these problems, a BM-SFO/PV-SFO double-layer memristor is designed in this work, in which the PV-SFO layer is an oxygen-rich interfacial intercalated layer, which can provide a large number of oxygen ions during the formation of CFs and withdraw these oxygen ions during the rupture of CFs. This allows the geometric size (e.g., diameter) of the CFs to be adjusted in a wide range, which is beneficial to obtaining continuously tunable, multiple resistance states. The RS behavior of the designed double-layer memristor is studied experimentally. Compared with the single-layer memristor, it exhibits good RS repeatability, small resistance fluctuation, small and narrowly distributed switching voltages. In addition, the double-layer memristor exhibits stable and gradual RS behavior, and hence it is used to emulate synaptic behaviors such as long-term potentiation and depression. A fully connected neural network (ANN) based on the double-layer memristor is simulated, and a recognition accuracy of 86.3% is obtained after online training on the ORHD dataset. Comparing with a single-layer memristor-based ANN, the recognition accuracy of the double-layer memristor-based one is improved by 69.3%. This study provides a new approach to modulating the performance of SFO-based memristors and demonstrates their great potential as artificial synaptic devices to be used in neuromorphic computing.