Synaptic Long-Term Potentiation (LTP), which is a long-lasting enhancement in signal transmission between neurons, is widely considered as the major cellular mechanism during learning and memorization. In this work, a NiOx-based memristor is found to be able to emulate the synaptic LTP. Electrical conductance of the memristor is increased by electrical pulse stimulation and then spontaneously decays towards its initial state, which resembles the synaptic LTP. The lasting time of the LTP in the memristor can be estimated with the relaxation equation, which well describes the conductance decay behavior. The LTP effect of the memristor has a dependence on the stimulation parameters, including pulse height, width, interval, and number of pulses. An artificial network consisting of three neurons and two synapses is constructed to demonstrate the associative learning and LTP behavior in extinction of association in Pavlov's dog experiment.