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In this paper, a dynamic model of an offshore drilling riser is developed based on the Hamilton principle. The developed dynamic model is transformed into a finite element model by introducing an approximate solution which chooses the Hermite cubic interpolation function of bending beam element as the shape function. Thereafter, the standard Newmark integration is applied to numerically simulate the dynamic responses of offshore drilling risers with varied system parameters, including the length of riser, top tension ratio, and buoyant factor. Based on the results of numerical simulation, under the influences of sea wind, sea current, and the periodic excitation of sea wave, the offshore drilling riser experiences a fast lateral deflection phase in the beginning, a reciprocating deflection phase in the following long duration, and then, a periodic oscillation when it reaches the dynamic stable condition, respectively. The riser system working in deeper water with a higher top tension ratio and a lower buoyant factor shows more controllable vibration and less lateral deflection. [ABSTRACT FROM AUTHOR]