Spiking neural network (SNN) has emerged as one of the most powerful brain-inspired computing paradigms in complex pattern recognition tasks that can be enabled by neuromorphic hardware. However, owing to the fundamental architecture mismatch between biological and Boolean logic, CMOS implementation of SNN is energy inefficient. A low-power approach with novel “neuro-mimetic” devices offering a direct mapping to synaptic and neuronal functionalities is still an open area. In this paper, SNN constructed with novel magnetic skyrmion-based leaky-integrate-fire (LIF) spiking neuron and the skyrmionic synapse crossbar is proposed. We perform a systematic device-circuit-architecture co-design for pattern recognition to evaluate the feasibility of our proposal. The simulation results demonstrated that our device has superior lower switching voltage and high energy efficiency, two times lower programming energy efficiency in comparison with CMOS devices. This work paves a novel pathway for low-power hardware design using full-skyrmion SNN architecture, as well as promising avenues for implementing neuromorphic computing schemes.