As important equipment for deep-sea oil and gas development, risers are subjected not only to external ocean environmental loads but also to internal drilling pipe contact collisions. In this study, a dynamic analysis model of the riser system considering the contact collision of drill pipe in drilling operation is established. Moreover, the contact stiffness method is used to describe the contact collision force between the drill pipe and riser. The model is discretized using the finite element method and solved using the Newmark-β method. The dynamic characteristics of the riser under the action of the marine environment and drilling conditions are analyzed. In addition, the corresponding safety protection measures are put forward for the contact collision between the drill pipe and riser. The results show that the collision force between drill pipe and riser is the largest in the initial period, and the contact form is gradually stable. The distribution of the collision force is basically consistent with that of the bending moment, and the collision force and collision probability are the largest near the water surface and at the flexible joint of the bottom end, which is easy to cause column wear failure. The collision force and collision probability of the drill pipe and riser increase with the increase of platform offset and sea current velocity but decrease with the increase of top tension and bit pressure. The increase of the top tension and the increase of the platform offset will reduce the contact area between the drill pipe and the riser.