For the linear equations system whose coefficient matrix is of -diagonal strictly dominance or doubly -chain diagonal strictly dominance, convergence properties of some iteration methods were studied and some convergence theorems were given, which solves the problem of spectral radius of iterative matrices. Results are applicable not only for -diagonal strictly dominance matrix or doubly diagonal strictly dominance matrices, but also for generalized strictly diagonally dominant matrices. Finally, numerical examples were given for illustrating advantage of results.