In this study, an improved eight-node quadrilateral finite element based on a twice-interpolation strategy (TIS) is given for correctly modeling the singular stress field near 2D crack tip of structures. In present approach, the approximation functions for interpolation strategy are established by using the TIS which included nodal values as well as averaged nodal gradients respectively. The stress intensity factors (SIFs) are therefore calculated following the proposed method. The accuracy of the proposed element and its numerical solutions are described by several examples.