  The influence of carbon concentration on the superconductivity (SC) in
MgC$_{x}$Ni$_3$ has been investigated by measuring the low temperature specific
heat combined with first principles electronic structure calculation. It is
found that the specific heat coefficient $\gamma_n=C_{en}/T$ of the
superconducting sample ($x\approx1$) in normal state is twice that of the
non-superconducting one ($x\approx 0.85$). The comparison of measured
$\gamma_n$ and the calculated electronic density of states (DOS) shows that the
effective mass renormalization changes remarkably as the carbon concentration
changes. The large mass renormalization for the superconducting sample and the
low $T_{c}$(7K) indicate that more than one kind of boson mediated
electron-electron interactions exist in MgC$_{x}$Ni$_3$.
