Synapse plays an important role in signal exchange and information encoding between neurons. Electric and chemical synapses are often used to investigate the synchronization in electrical activities of neurons. In this paper, memristor is used to connect two neurons and the phase synchronization in electrical activities is discussed. Inter-spike interval (ISI) is calculated from the sampled time series for membrane potential, and the dependence of coupling intensity on phase synchronization of neuron is investigated and the effect of electromagnetic induction is considered. Furthermore, the synchronization stability of network is detected under noise; a statistical synchronization factor is also calculated. It is found synchronization can be enhanced under memristor coupling and appropriate noise is also helpful for synchronization stability.