Neuromorphic computing inspired by the neural systems in human brain will overcome the issue of independent information processing and storage. An artificial synaptic device as a basic unit of a neuromorphic computing system can perform signal processing with low power consumption, and exploring different types of synaptic transistors is essential to provide suitable artificial synaptic devices for artificial intelligence. Hence, for the first time, an electret-based synaptic transistor (EST) is presented, which successfully shows synaptic behaviors including excitatory/inhibitory postsynaptic current, paired-pulse facilitation/depression, long-term memory, and high-pass filtering. Moreover, a neuromorphic computing simulation based on our EST is performed using the handwritten artificial neural network, which exhibits an excellent recognition accuracy (85.88%) after 120 learning epochs, higher than most reported organic synaptic transistors and close to the ideal accuracy (92.11%). Such a novel synaptic device enriches the diversity of synaptic transistors, laying the foundation for the diversified development of the next generation of neuromorphic computing systems.