We investigated superconducting property of ($Mg_{1-x}$$Zn_{x}$)$CNi_3$ (x=0,0.03, 0.06, 0.09, 0.12, 0.15, and 0.18) sample where Mg is substituted with Zn. The samples were synthesized us ins the solid state reaction method under As atmosphere. X -ray diffraction spectra show that the $MgCNi_3$ structure is maintained up to x=18. With increasing x, the lattice constant (or the Ni-Ni distance) decreases. Magnetic susceptibility measurement shows that $T_{c}$ decreases systematically with x and becomes ～2K at x =0.18. Surprisingly, the transition width remains sharp (～0.3K). Under some assumptions, we estimate the coupling constant in the McMillan formula as a function of x which we interpret in terms of the BCS theory.y.y.y.