In a neural network, neuron computation is achieved through the summation of input signals fed by synaptic connections. The synaptic activity (weight) is dictated by the synchronous firing of neurons, inducing potentiation/depression of the synaptic connection. This learning function can be supported by the resistive switching memory (RRAM), which changes its resistance depending on the amplitude, the pulse width and the bias polarity of the applied signal. This work shows a new synapse circuit comprising a MOS transistor as a selector and a RRAM as a variable resistance, displaying spike-timing dependent plasticity (STDP) similar to the one originally experienced in biological neural networks. We demonstrate long-term potentiation and long-term depression by simulations with an analytical model of resistive switching. Finally, the experimental demonstration of the new STDP scheme is presented.