In this work, we propose a new memristor SPICE model that accounts for the typical synaptic characteristics that have been previously demonstrated with practical memristive devices. We show that this model could account for both volatile and non-volatile memristance changes under distinct stimuli. We then demonstrate that our model is capable of supporting typical STDP with simple non-overlapping digital pulse pairs. Finally, we investigate the capability of our model to simulate the activity dependence dynamics of synaptic modification and present simulated results that are in excellent agreement with biological results.