Abstract: In the paper, a novel enriched function for those elements containing crack tip is proposed. By the method of trigonometric transform, the four crack tip enriched functions in the standard extended finite element methods (XFEM) are reduced to the two ones. The reduced enriched functions still keep the two properties, such as the stress singular at the crack tip and the discontinuities of crack surfaces. The enriched degrees of freedom for those nodes of element containing crack tip is thereby reduced from 8 to 4. The two orthogonal level set functions are used to represent the existing crack in materials. The method for identifying the enriched type of elements is described in details. An integration schemes for enriched elements are given. Finally, several classic fracture problems are given to verify the numerical precision of the proposed crack tip enriched functions. The results show the effectiveness of the proposed method.