In this paper, synchronous dynamic behavior of three Ringcoupled and Linearcoupled HR neuronal system is examined. Through constructing a suitable Lyapunov function as well as applying linear matrix inequalities and matrix theory, the global exponential stability and the global asymptotic stability of linearised error system at zero solution is obtained, respectively, and the relative criterion is theoretically provided for global asymptotic synchronization and global exponential synchronization of HR neuronal system. Furthermore, Ringcoupled network is synchronized more easily than Linearcoupled network. Numerical simulations also verifies the effectiveness of the results in this paper.