  The quadrupole normal-mode oscillation frequency $f_{n}$ of multiquark star
are computed for $n=1-5$. At the transition from low to high density multiquark
in the core region, the first 2 modes jump to larger values, a distinctive
signature of the presence of the high-density core. When the star oscillation
couples with spacetime, gravitational waves~(GW) will be generated and the star
will undergo damped oscillation. The quasinormal modes~(QNMs) of the
oscillation are computed using two methods, direct scan and WKB, for QNMs with
small and large imaginary parts respectively. The small imaginary QNMs have
frequencies $1.5-2.6$ kHz and damping times $0.19-1.7$ secs for multiquark star
with mass $M=0.6-2.1 M_{\odot}$~(solar mass). The WKB QNMs with large imaginary
parts have frequencies $5.98-9.81$ kHz and damping times $0.13-0.46$ ms for
$M\simeq 0.3-2.1 M_{\odot}$. They are found to be the fluid $f-$modes and
spacetime curvature $w-$modes respectively.
