Memristive technologies are attractive due to their non-volatility, high-density, low-power and compatibility with CMOS. For memristive devices, a model corresponding to practical behavioral characteristics is highly favorable for the realization of its neuromorphic system and applications. This paper presents a novel flexible memristor model with electronic resistive switching memory behavior. Firstly, the Ag-Au / MoSe2-doped Se / Au-Ag memristor is prepared using hydrothermal synthesis method and magnetron sputtering method, and its performance test is conducted on an electrochemical workstation. Then, the mathematical model and SPICE circuit model of the Ag-Au / MoSe2-doped Se / Au-Ag memristor are constructed. The model accuracy is verified by using the electrochemical data derived from the performance test. Furthermore, the proposed model is applied to the circuit implementation of spiking neural network with biological mechanism. Finally, computer simulations and analysis are carried out to verify the validity and effectiveness of the entire scheme.