This paper presents an adaptive neural network (NN) sliding mode control for synchronization of inhibitory coupled Hindmarsh-Rose (HR) neurons. A single HR neuron may exhibit spike-burst chaotic behaviors. Inhibitory coupling makes two HR neurons behaves in anti-phase quasi-synchronization mode. We first derive the sliding mode controller via active control strategy. Then, a simple radial basis function (RBF) NN is designed to approximate the uncertain nonlinear part of the error dynamical system which has been assumed to be available in the active control. The weights of the NN are tuned on-line based on the sliding mode reaching law. According to the Lyapunov stability theory, the stability of the closed-loop error system is guaranteed. Synchronization is obtained by proper choice of the control parameters. The simulation results demonstrate the effectiveness of the proposed control method.