In this work, an RRAM device with the structure of Ag/MXene/MXene/Pt was fabricated, and stacked solution-processed MXene layers acted as the resistive switching (RS) layer. The device exhibited bipolar RS performance with the operation voltage lower than 2.5 V and the switching ratio around 103. The multi-level states of conductance indicated the bionic synaptic characteristics of this device. A performance like long-term potentiation and depression (LTP/LTD) response suggested the great potential of this device in the neuromorphic system. In addition, based on the MNIST dataset, the pattern recognition system with key parameters from LTP/LTD showed the result with 85% recognition accuracy. After modulation on non-linearity of LTP and LTD curves, higher recognition accuracy was obtained, which was around 93%.