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Novel skyrmion-magnetic tunnel junction (SK-MTJ) devices were investigated for the first time to implement the ternary neural networks (TNN). In the SK-MTJ, an extra magnetoresistance state beyond binary parallel and anti-parallel MTJ states was achieved by forming a skyrmion vortex structure in the free layer. Based on the SK-MTJ, we propose a synaptic architecture with bit-cell design of +1, 0, and -1 to replace the full precision floating point arithmetic with equivalent bit-wise multiplication operation. To explore the feasibility of the SK-MTJ-based synaptic devices for TNN application, circuitlevel simulations for image recognition task were conducted. The recognition rate can reach up to 99% with 5% device variation and an average power consumption of 29.23 μW.