Neuromorphic engineering is a promising computing paradigm in next-generation information and communication technology. In particular, spiking neural networks are expected to reduce power consumption drastically owing to their event-driven operation. The spike-timing-dependent plasticity (STDP) rule, which learns from local spike-timing differences between spiking neurons, is a biologically plausible learning rule for spiking neural networks (SNNs). In this study, we designed and simulated an analog circuit that reproduces the multiplicative STDP rule, which is more flexible and adaptive to external signals. We also derived analytical expressions for the behavior of the proposed circuit. These results provide important insights for designing energy efficient neuromorphic devices for applications including edge computing.