  We report on the valence fluctuation of Ce in CeMo$_{2}$Si$_{2}$C as studied
by means of magnetic susceptibility $\chi(T)$, specific heat $C(T)$, electrical
resistivity $\rho(T)$ and x-ray absorption spectroscopy. Powder x-ray
diffraction revealed that CeMo$_{2}$Si$_{2}$C crystallizes in
CeCr$_{2}$Si$_{2}$C-type layered tetragonal crystal structure (space group
\textit{P4/mmm}). The unit cell volume of CeMo$_{2}$Si$_{2}$C deviates from the
expected lanthanide contraction, indicating non-trivalent state of Ce ions in
this compound. The observed weak temperature dependence of the magnetic
susceptibility and its low value indicate that Ce ions are in valence
fluctuating state. The formal $L_{III}$ Ce valence in CeMo$_{2}$Si$_{2}$C
$<$$\widetilde{\nu}$$>$ = 3.11 as determined from x-ray absorption spectroscopy
measurement is well bellow the value $<$$\widetilde{\nu}$$> \simeq$ 3.4 in
tetravalent Ce compound CeO$_{2}$. The temperature dependence of specific heat
does not show any anomaly down to 1.8 K which rules out any magnetic ordering
in the system. The Sommerfeld coefficient obtained from the specific heat data
is $\gamma$ = 23.4 mJ/mol\,K$^{2}$. The electrical resistivity follows the
$T{^2}$ behavior in the low temperature range below 35 K confirming a Fermi
liquid behavior. Accordingly both the Kadowaki Wood ratio $A/\gamma^{2}$ and
the Sommerfeld Wilson ratio $\chi(0)/\gamma$ are in the range expected for
Fermi-liquid systems. In order to get some information on the electronic
states, we calculated the band structure within the density functional theory,
eventhough this approach is not able to treat 4f electrons accurately. The
non-$f$ electron states crossing the Fermi level have mostly Mo 4d character.
They provide the states with which the 4f sates are strongly hybridized,
leading to the intermediate valent state.
