Magnetic skyrmions are promising candidates for next-generation information carriers, owing to their small size, topological stability, and ultralow depinning current density. A wide variety of skyrmionic device concepts and prototypes have been proposed, highlighting their potential applications. Here, we report on a bioinspired skyrmionic device with synaptic plasticity. The synaptic weight of the proposed device can be strengthened/weakened by positive/negative stimuli, mimicking the potentiation/depression process of a biological synapse. Both short-term plasticity(STP) and long-term potentiation(LTP) functionalities have been demonstrated for a spiking time-dependent plasticity(STDP) scheme. This proposal suggests new possibilities for synaptic devices for use in spiking neuromorphic computing applications.