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 recently been proposed, highlighting their potential applications. Furthermore, the intrinsic properties of skyrmions enable new functionalities that may be inaccessible to conventional electronic devices. Here, we report on a skyrmion-based artificial synapse device for neuromorphic systems. 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 and long-term potentiation functionalities have been demonstrated with micromagnetic simulations. This proposal suggests new possibilities for synaptic devices in neuromorphic systems with adaptive learning function.