Fast multipole boundary element method (FM-BEM) is applied in three-dimensional elastic contact problem, but the singular integral influence calculation efficient. How to solve singular integral is become an important problem for improving FM-BEM. In this paper, Taylor series expansion and Laplace transformation were introduced; it can be used to improve the singular integral. After Laplace transformation, the singular integral is written as exponential series form, which can be suit for fast multipole method. It is not only solving singularity, but also suit fast calculation. This method improves the calculation time and calculation accurate of FM-BEM.