With the advent of artificial intelligence (AI), memristors have received significant interest as a synaptic building block for neuromorphic systems, where each synaptic memristor should operate in an analog fashion, exhibiting multilevel accessible conductance states. Here, we demonstrate that the transition of the operation mode in poly(1,3,5-trivinyl-1,3,5-trimethyl cyclotrisiloxane) (pV3D3)-based flexible memristor from conventional binary to synaptic analog switching can be achieved simply by reducing the size of the formed filament. With the quantized conductance states observed in the flexible pV3D3 memristor, analog potentiation and depression characteristics of the memristive synapse are obtained through the growth of atomically thin Cu filament and lateral dissolution of the filament via dominant electric field effect, respectively. The face classification capability of our memristor is evaluated via simulation using an artificial neural network consisting of pV3D3 memristor synapses. These results will encourage the development of soft neuromorphic intelligent systems.