In order to improve the walking stability of a semi-passive biped robot on horizontal ground, the walking dynamic behavior of the semi-passive biped robot under impulse thrust is studied. Taking the simplest special walking model as the dynamic model, the impulse thrust of the heel of the stance leg is used as the walking power source of the biped robot. In view of the highly nonlinear of the system model, the nonlinear differential equation in continuous phase is linearized. A two-dimensional discrete map is constructed by using the conservation of angular momentum and impulse thrust. The existence and stability of the periodic gait of the system are analyzed by using the fixed points and their eigenvalues of the discrete map. The period-doubling bifurcation of the system is discussed. On the basis of theoretical analysis, the walking dynamics of the semi-passive biped robot is simulated by Matlab software. The simulation experiment shows that the semi-passive biped robot walking on the horizontal ground has stable period-1 gait and period-2 gait.