The close replication of synaptic functions is an important objective for achieving a highly realistic memristor-based cognitive computation. The emulation of neurobiological learning rules may allow the development of neuromorphic systems that continuously learn without supervision. In this work, the Bienenstock-Cooper-Munro learning rule, as a typical case of spike-rate-dependent plasticity, is mimicked using a generalized triplet-spike-timing-dependent plasticity scheme in a WO3-x memristive synapse. It demonstrates both presynaptic and postsynaptic activities and remedies the absence of the enhanced depression effect in the depression region, allowing a better description of the biological counterpart. The threshold sliding effect of Bienenstock-Cooper-Munro rule is realized using a history-dependent property of the second-order memristor. Rate-based orientation selectivity is demonstrated in a simulated feedforward memristive network with this generalized Bienenstock-Cooper-Munro framework. These findings provide a feasible approach for mimicking Bienenstock-Cooper-Munro learning rules in memristors, and support the applications of spatiotemporal coding and learning using memristive networks.