The smooth-and-discontinue(SD) oscillator with time-dependent stiffness was put forward and founded to study dynamic characteristics of beam bridge under moving load. Mid-span deflection of beam bridge under moving load was described as vibration trace. Proper stiffness model function was elected and study nonlinear dynamic behaviors of mid-span deflection when several vehicles pass through bridge successively. The software MATLAB was used to simulate the model and obtain the bifurcation diagrams with parameter of vehicle speed and Poincare sections of the vehicle-bridge coupled system. The result shows the complicated nonlinear dynamics with periodic motion, quasi-periodic motion phenomena and chaos, the occurrence alternatively among these motions.