The periodic solution and its period of spontaneous firing of a neuronal RoseHindmarsh (RH) model, were calculated by a modified shooting method, which can calculate the periodic orbit and its period of the autonomous nonlinear dynamic system. The Floquet multipliers of the periodic solutions were calculated, and the bifurcations of periodic solutions including period doubling bifurcation and saddlenode bifurcation were also analyzed. The results are helpful for understanding the dynamical and biological significances of transition between periodic firing patterns.