Abstract: In the simulation of lattice gauge theory，RHMC algorithm is an accurate algorithm which can be

used to any number of fermions. Its central idea is to expand the fermion determinant into rational functions，the implementation

of this algorithm results in a lot of matrix inversion of fermion matrix，and brings about numerous time

and resources consumption. Therefore，its use is limited. This paper uses the shifted polynomial to obtain an approach

　　to solve this problem for the conjugate gradient method. This approach can be applied into RHMC algorithm.

Key words: fermions, inverse matrix, lattice gauge theory, shifted polynomial