The r-mode instability window of low-mass strange stars is studied using the modified bag model of strange quark matter and reasonable sets of parameters. The results show that the spin frequency limit of strange stars increases with the decrease of their mass, and the highest observed spin frequency(716 Hz) of pulsars can be explained if the strange star mass is lower than about 0.1-0.2 M⊙, depending on the parameters of the equation of state.