Since the experimental discovery of magnetic skyrmions achieved one decade ago, there have been significant efforts to bring the virtual particles into all-electrical fully functional devices, inspired by their fascinating physical and topological properties suitable for future low-power electronics. Here, we experimentally demonstrate such a device: electrically-operating skyrmion-based artificial synaptic device designed for neuromorphic computing. We present that controlled current-induced creation, motion, detection and deletion of skyrmions in ferrimagnetic multilayers can be harnessed in a single device at room temperature to imitate the behaviors of biological synapses. Using simulations, we demonstrate that such skyrmion-based synapses could be used to perform neuromorphic pattern-recognition computing using handwritten recognition data set, reaching to the accuracy of ~89 percents, comparable to the software-based training accuracy of ~94 percents. Chip-level simulation then highlights the potential of skyrmion synapse compared to existing technologies. Our findings experimentally illustrate the basic concepts of skyrmion-based fully functional electronic devices while providing a new building block in the emerging field of spintronics-based bio-inspired computing.