The resistive switching behavior of polycrystalline BiFeO3 films was investigated, and the coexistence of analog and digital resistive switching behaviors in a single Pt/BiFeO3/Pt device was discovered. Without electroforming, the Pt/BiFeO3/Pt device showed analog switching characteristics with a resistance ratio greater than 10; however, after electroforming, the device exhibited digital bipolar resistive switching features. It is suggested that the charge trapping/detrapping is crucial in the analog resistive switching, while the conductive filament can account for the digital switching. Additionally, a physical model is proposed to disclose the diffusion kinetics of oxygen vacancies in the memristive behaviors of the device. This work opens up a way in designing multi-functional memristive devices, which could be an ideal solution for the neuromorphic computation, non-volatile information storage and logic operation. (C) 2016 Elsevier B.V. All rights reserved.