This paper proposes a novel computationally efficient dynamics modeling approach for down-hole well drilling system. The existing drilling modeling methods are either computationally intensive such as those using finite element method (FEM) or weak in fidelity for complex geometry such as those using transfer matrix method (TMM). To take advantage of the benefits of FEM and TMM and avoid their drawbacks, this paper presents a new hybrid method integrating both of the aforementioned modeling approaches, enabled by the unique structural geometry of the drilling system. The new method is then applied to the down-hole well drilling system modeling, incorporating the dynamics of top drive, drill-string, bottom-hole-assembly (BHA), and bitrock interaction. The hybrid integration approaches for both the axial and torsional dimensions are explicitly derived, and we also give directions on how to resolve those for flexural dimension. To this end, numerical simulation results are presented to demonstrate the effectiveness of the proposed hybrid modeling approach.