Abstract: Complete synchronization of two mutually coupled identical chaotic Hindmarsh-Rose neurons model with gap junction was studied. Gap junction isalso called electrical coupling, it acts as one of the main communications between neurons in nervous systems, its most important role is to make a large ensembles of neurons emit synchronous firing rhythm patterns.The traditional method to investigate complete synchronization was using numerical simulations, such as the conditional Lyapunov exponents, but it was lack of theoretical foundation and can only offer us a necessary condition to guarantee the occurrence of complete synchronization. Based on the conditional Lyapunov exponents method, synchronization of more coupled neurons is hard to be studied. So two new methods of Lyapunov function method and mode decomposition method here was introduced, and if and only if condition and the sufficient condition will be given. These methods are efficient to deal with more coupled neurons and nonsymmetrical coupling schemes, the validity of them was tested by numerical simulation.