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Short- and long-term neuroplasticity behaviors are key mechanisms for various activities. In this paper, we propose a synaptic transistor with a floating-gate (FG) node and an amorphous InGaZnO (IGZO) channel layer. The proposed device emulates the neuroplasticity functions of both short-term memory (STM) and long-term memory (LTM) through the control of the amplitude and the number of input pulses. The STM operated by ion movement in the gate dielectrics occurs when the input amplitude is relatively small (< 9 V). The LTM operated through the storage of electrons in the FG occurs when the input amplitude is relatively large (>10 V). In addition, as the number of input pulses increases, information is stored for a longer time. Our FG IGZO synaptic transistor could be a promising device solution for brain-inspired computing systems.