A kind of Incomplete Generalized Minimal Residual Method (IGMRES(m)) based on the Fast Multipole Boundary Element Method (FM-BEM) was proposed, which was a new program-iteration pattern algorithm. By using the truncation technology, the presented algorithm constructed new recursion formulae only using some of the calculated vectors to compute the following vectors, which could greatly reduce the computation and memory requirement. The Fast Multipole Method (FMM) was used to compute the product of a matrix and some vectors. Numerical experiments proved that the new algorithm was highly efficient to compute the elasto-plastic frictional contact problems especially with complicated iteration and time-consuming calculation. And it could greatly reduce the iteration times and improve the computational efficiency with ensured numerical accuracy.