A synaptic device that functionally mimics a biological synapse is a promising candidate for use as an electronic element in a neuromorphic system. In this study, flexible electronic synaptic devices based on poly (methyl methacrylate) (PMMA):CdSe/CdZnS core-shell quantum-dot (QD) nanocomposites are demonstrated. The current-voltage characteristics for the synaptic devices under consecutive voltage sweeps show clockwise hysteresis, which is a critical feature of an artificial synaptic device. The effect of the CdSe/CdZnS QD concentration on the device performance is studied. The flexible electronic synaptic devices under bending show the similar and stable electrical performances. The memory retention measurements show that the e-synapse exhibits long-term potentiation and depression. The carrier transport mechanisms are analyzed, and thermionic emission and space-charge-limited-current conduction are found to be dominant.