Summary: A second-order ordinary differential system with a parameter is considered. The stability of the equilibrium and the existence condition of Hopf bifurcation are studied by analyzing the distribution of the characteristic roots of the linearized equation. The system is discretized by the Newmark method. By analyzing the distribution of the characteristic roots of the discrete system, a pair of parameters are determined such that the discrete system undergoes a Neimark-Sacker bifurcation for any time steps. On the contrary, it is proven that if there exists a Neimark-Sacker bifurcation for the discrete system, then the continuous system undergoes a Hopf bifurcation. Finally, some numerical simulations are given to show the accuracy of our theoretical analysis.