The spike-timing-dependent synaptic plasticity (STDP) is a form of change of a synaptic weight depending on timings of pre- and postsynaptic spikes. In this brief, a novel asynchronous cellular automaton model of the STDP is presented. It is shown that the presented model can reproduce various STDP characteristics observed in physiological experiments. Also, the presented model is implemented in a field-programmable gate array, and laboratory experiments validate the reproductions of the physiological STDP characteristics. It is then shown that the presented model consumes much less hardware resources than a computationally efficient differential equation model of the STDP.