The modeling of three-phase fluid flow has many important applications in reservoir simulation. In this paper, we introduce a high order method for sequentially solving the phase pressure-saturation formulation of three-phase flow. The sequential approach, while less stable than a fully coupled approach, is more computationally efficient. We present a discontinuous Galerkin method in space, suitable for the sequential approach due to its high-order accuracy. We consider coarser meshes with high degree polynomials to minimize the dimension of the system while maximizing accuracy. Numerical results are given for homogeneous media.