The first black-phosphorus synaptic device is demonstrated, which offers intrinsic anisotropy in its synaptic characteristics directly resulting from its low crystalline symmetry. Key features of biological synapses, such as long-term plasticity with heterogeneity, including long-term potentiation/depression and spike-timing-dependent plasticity, are mimicked. This demonstration represents an important step toward introducing intrinsic heterogeneity to artificial neuromorphic systems.