This paper employs the cross-currency LIBOR market model to price five types of quanto interest rate exchange options, namely, domestic swap rate vs. foreign Swap rate, domestic swap rate vs. foreign LIBOR rate, domestic LIBOR rate vs. foreign swap rate, foreign swap rate vs. foreign swap rate and foreign swap rate vs. foreign LIBOR rate. A new approach to approximate the distribution of a (foreign) forward swap rate under the cross-currency LIBOR market model is presented and employed to price quanto interest rate derivatives involved with constant-maturity swap rates. As compared with Monte Carlo simulation, the numerical examples show that the resulting pricing formulas are sufficiently and robustly accurate.