A memristor with analogue resistive switching (RS) memory behaviors could provide enough conductance states for high-efficiency neuromorphic computing because this type RS memory feature can avoid conductance clamping, steeply change, and computing invalidation. Simulating the behavior of biological synapses under stimulus pulse can better reveal the bionic characteristic mechanism of electronic devices and provide support for high performance neuromorphic computation. Synaptic paired-pulse facilitation (PPF) is an important characteristic of biological synapses, reflecting the facilitation and adaptation process under external stimuli, which is crucial to reveal the working mechanism of neurons. A memristor with the structure of the Ag/FeO_x/ITO was prepared by RF magnetron sputtering, which was designed by energy band engineering for the PPF demonstration. Experimental measurement of the electric properties illustrates that the developed memristor displays an excellent asymptotic nonlinear resistance switching behaviors, which is so called analogue RS memory behavior. Importantly, this developed memristor presents this analogue RS memory behavior during 3000 I-V sweepings, provides dissociable 16 conductance states that could be well maintained for 10⁴ s, illustrating that these available conductance states are nonvolatile. Based on the energy band structure and oxygen vacancy (V_O) defects, a physical mechanism, which involved trap sites softly filled by the injection electron, electron tunneling between the potential barrier built by the contact of Ag/FeO_x and FeO_x/ITO, and the V_O migration that accompanied a volatile feature to some extent, is proposed to comprehend the observed analogue RS memory behaviors. According to this mechanism, a typical PPF feature is obtained after modulating the voltage pulse width and amplitude. The observed analogue RS memory behaviors and PPF behaviors show a promising potential and advantage in neuromorphic computing.