  An iterative formula for the Kostka-Foulkes polynomials is given using the
vertex operator realization of the Hall-Littlewood polynomials. The operational
formula can handle large Kostka-Foulkes polynomials, and a stability property
for the Kostka-Foulkes polynomials is shown. We also use our algorithm to give
a formula of $K_{\lambda\mu}(t)$ for $\mu$ being hook-shaped.
