In order to realize the dimension upgrade of Embedded discrete fracture model (EDFM), and make EDFM effective for arbitrary-shape inclined fractures, this paper presents a 3D EDFM pre-processing algorithm for arbitrary-shape fractures, which provides a specific idea to solve the key difficulty of dimension upgrade of EDFM. Then, according to the pre-processing algorithm, a 3D EDFM adaptive to arbitrary-shape inclined fractures is realized, and a corresponding numerical example is implemented to illustrate the validness of proposed algorithm.