We propose a new memristive model for the neuronal synapse based on the spike-timing-dependent plasticity (STDP) protocol, considering both long-term and short-term plasticity in the synapse. Higher-order behavior is modeled by a memristor with adaptive thresholds, which realizes the well-established suppression principle of Froemke. We assume a mechanism of variable thresholds adapting to synaptic potentiation (LTP) and depression (LTD), which reproduces the refractory time in the weight modification. The corresponding dynamical process is governed by a set of ordinary differential equations. Interestingly, the Froemke's model and our memristive model, based on two completely different mechanisms, are found to be quantitatively equivalent for the 'pre-post-pre' case and 'post-pre-post' case. A relation of the adaptive thresholds to short-term plasticity is addressed.