A FORTRAN subroutine called GRSIM subroutine is presented for the iterative solution of a set of non-symmetric linear equations, $Ax = b$, where the coefficient matrix $A$ is a sparse nearly symmetric structured $M$-matrix. These matrices occur repeatedly in the finite-difference solution of partial differential equations. The method solves non-symmetric systems of linear equations, but uses highly developed techniques for the solution of symmetric systems of linear equations. A general description of the method, which is based on particular class of regular splitting, is given. The GRSIM subroutine uses a regular splitting and the convergence is, therefore, guaranteed.