This paper presents a dynamics model for the down-hole directional drilling system based on a hybrid modeling method with model order reduction. Due to the long dimensionality of the drill string, a drilling model based on pure numerical methods such as the finite element method (FEM) may require a large number of meshes, which induces high computational intensity. By using a hybrid method combining FEM and the transfer matrix method (TMM), the order of the model can be significantly reduced. To further reduce the modeling order, a Proper Orthogonal Decomposition (POD)-Galerkin projection based approach is applied, and a set of linear normal modes (LNMs) are identified to create a reduced order projection subspace. To this end, simulation results are presented to prove that the method can effectively capture the dominant modes of the drilling dynamics, and a computationally-efficient and high-fidelity reduced order hybrid model can be reached for real-time state estimation and control design.