Two-stage iterative method is comprised by the inner and outer iteration and the numbers of inner iteration. We find out an upper bound of R₁-factor of two-stage iterative methods for solution of linear systems. And the upper bound is expressed applying the R₁-factors of the inner and outer iteration and the numbers of the inner iteration; the premier parts of the upper bound is the R₁-factor of outer iteration. Furthermore, for any inner iteration method and any numbers of the inner iteration, it is also showed that the lower bound of the R₁-factor of the two-stage iterative method can also be given by the R₁-factor of the outer iteration in the case of monotone matrices. The results indicate the effects of convergence rates of the inner and outer iteration and the numbers of inner iteration on the convergence rates of the two-stage iterative method.