Emerging nonvolatile memory technologies have been much studied to realize massively interconnected Spiking Neural Networks (SNNs) due to its high density, and energy efficiency. Nevertheless, most of the previous studies on utilizing such technologies have focused on implementing a traditional pair-based Spike Timing Dependent Plasticity (STDP) rule, which turned out to fail to reproduce multiple physiological experimental results. In this paper, we present a neuromorphic circuit for a three-terminal spintronic synapse with a triplet-based STDP rule, which is a higher order of learning mechanism. Simulation results indicate that the proposed learning circuit for the triplet-based STDP rule significantly improves learning capability in mimicking the various biological experimental data. We introduce a normalized mean-square error E value to evaluate the performance of each of the learning circuits quantitatively. The proposed learning circuit achieves E value of 1.77, which is far better than the conventional one that achieves E value of 12.2.