In this thesis, we analyze a numerical method for hypersingular integrals. Based on classical results, we develop the Gauss-Laguerre method for such kind of hypersingular integral: ∫∞₀[f(x)/(x-t)²]e⁻ˣdx. This thesis is divided into three chapters. An introduction to hypersingular integral and a brief analysis of the numerical methods for hypersingular integrals are given by Chapter 1. In Chapter 2,we give a brief introduction to Laguerre polynomial and the Gauss-Laguerre method. In Chapter 3, we develop a degree result and an estimate of the error. The numerical test of the Gauss-Laguerre method is also given.