In this work, we propose a synaptic transistor that uses photoactive organic semiconductors for floating-gate and channel to modulate synaptic weights. Applying a 60 V gate bias to the proposed device traps charge in the floating-gate, resulting in an increased conductance. Therefore, the conductance changed by a constant gate bias stimulus can be expressed as a synaptic weight. On the other hand, a -60 V gate bias is insufficient to remove trapped carriers, so we utilize a photoactive floating-gate. Simultaneous application of light and gate voltage bias to the synaptic transistor removes the trapped carriers and resets the conductance to its initial state. Applying this synaptic transistor behavior to a neuromorphic application, we designed and trained a single-layer neural network schematic consisting of 784 input neurons, 10 output neurons, and 7,840 synapses. As a result, we conducted handwriting recognition tests with the trained neural network and achieved an accuracy of up to 88.74%.