  We study the decays of the anti-triplet charmed baryon state
$(\Xi_c^0,\Xi_c^+,\Lambda_c^+)$ based on the $SU(3)$ flavor symmetry. In
particular, after predicting ${\cal B}(\Xi_c^0\to \Xi^-\pi^+)=(15.7 \pm
0.7)\times 10^{-3}$ and ${\cal B}(\Xi_c^+\to\Xi^-\pi^+\pi^+)=(14.7\pm
8.4)\times 10^{-3}$, we extract that ${\cal B}(\Xi_c^0\to\Lambda
K^-\pi^+,\Lambda K^+K^-,\Xi^- e^+\nu_e)=(16.8\pm 2.3,0.45\pm 0.11,48.7\pm
17.4)\times 10^{-3}$ and ${\cal B}(\Xi_c^+\to p K_s^0 K_s^0,\Sigma^+
K^-\pi^+,\Xi^0\pi^+\pi^0,\Xi^0 e^+\nu_e)=(1.3\pm 0.8,13.8\pm 8.0,33.8\pm
21.9,33.8^{+21.9}_{-22.6})\times 10^{-3}$. We also find that ${\cal
B}(\Xi_c^0\to \Xi^{0} \eta,\Xi^{0} \eta')=(1.7 ^{+ 1.0 }_{- 1.7 },8.6 ^{+ 11.0
}_{-\;\,6.3 })\times 10^{-3}$, ${\cal B}(\Xi_c^0\to \Lambda^{0}
\eta,\Lambda^{0} \eta')=(1.6 ^{+ 1.2 }_{- 0.8 },9.4 ^{+ 11.6 }_{-\;\,6.8
})\times 10^{-4}$ and ${\cal B}(\Xi_c^+\to \Sigma^{+} \eta,\Sigma^{+}
\eta')=(28.4 ^{+ 8.2 }_{- 6.9 },13.2 ^{+ 24.0 }_{- 11.9 })\times 10^{-4}$.
These $\Xi_c$ decays with the branching ratios of $O(10^{-4}-10^{-3})$ are
clearly promising to be observed by the BESIII and LHCb experiments.
