A drilling riser is a connecting channel in deep water drilling technology. The riser may undergo significant axial vibrations during disconnection, which in turn can lead to failure. In order to investigate the longitudinal vibration behavior of a drilling riser, we constructed a mathematical model based on the classical wave equations, solved using a finite-difference method. We have simulated the longitudinal vibration parameters for a riser under production conditions in the South China Sea as a function of location, top tension, damping coefficient, lower marine riser package (LMRP) weight, riser inner diameter, and riser length. The research results showed that longitudinal vibration increases with distance from the water surface to the LMRP and the vibration amplitude also increases with increasing top tension, riser inner diameter, and riser length, and decreases with increasing LMRP weight. As the damping coefficient increases, over time the vibration amplitude decreases compared with the initial value.