In order to calculate the stress intensity factors of two-dimensional cracks emanating from elliptical hole, a solution method for stress intensity factor based on Muskhelishvili complex function theory and truncated conformal mapping approach is proposed in this paper. Firstly, the conformal mapping function formed by the transcendental function is expanded into a series with finite terms, and then the stress function is derived by using the complex function theory, so as to solve the mixed-mode stress intensity factors for two cracks of arbitrary length from an elliptical hole. Compared with other methods, the presented method is more applicable and efficient, the results are reliable. The results of examples show that the non-dimensional stress intensity factors for double cracks from an elliptical hole are under comprehensive impact of the elliptical hole semi-axes ratio, crack length and angle.