  Recently, it has been reported that a candidate for a quark star may have
been observed. In this article, we pay attention to quark stars with radiation
radii in the reported range. We calculate nonradial oscillations of $f$-, $w$-
and $w_{\rm II}$-modes. Then, we find that the dependence of the $f$-mode
quasi-normal frequency on the bag constant and stellar radiation radius is very
strong and different from that of the lowest $w_{\rm II}$-mode quasi-normal
frequency. Furthermore we deduce a new empirical formula between the $f$-mode
frequency of gravitational waves and the parameter of the equation of state for
quark stars. The observation of gravitational waves both of the $f$-mode and of
the lowest $w_{\rm II}$-mode would provide a powerful probe for the equation of
state of quark matter and the properties of quark stars.
