  In this paper, we analyze the light variations of KIC 10975348 using
photometric data delivered from $Kepler$ mission. This star is exceptionally
faint ($K_{p}$ = 18.6 mag), compared to most well-studied $\delta$ Scuti stars.
The Fourier analysis of the short cadence data (i.e. Q14, Q15 and Q16, spanning
220 days) reveals the variations are dominated by the strongest mode with
frequency F0 = 10.231899 $\rm{d^{-1}}$, which is compatible with that obtained
from $RATS-Kepler$. The other two independent modes with F1 (= 13.4988
$\rm{d^{-1}}$) and F2 (= 19.0002 $\rm{d^{-1}}$) are newly detected and have
amplitudes two orders of magnitude smaller than F0. We note that, for the first
time, this star is identified to be a high-amplitude $\delta$ Sct (HADS) star
with amplitude of about 0.7 mag, and the lower ratio of F0/F1 = 0.758 suggests
it might be a metal-rich variable star. The frequency F2 may be a third
overtone mode, suggesting this target might be a new radial triple-mode HADS
star. We perform $O - C$ analysis using 1018 newly determined times of maximum
light and derive an ephemeris formula: $T_{max}$ =
2456170.241912(0)+0.097734(1) $\times$ $E$. The $O - C$ diagram shows that the
pulsation period of KIC 10975348 seems to show no obvious change, which is in
contrast to that of the majority of HADS stars. The possible cause of that may
be due to the current short time span of observations. To verify its possible
period variations, regular observation from space with a longer time span in
future is needed.
