The surface electronic structures of ${\mathrm{MgCNi}}_{3}(001)$ with both the MgNi terminated (MgNi-Term) and the CNi terminated (CNi-Term) surfaces were investigated using the all-electron full-potential linearized augmented plane-wave method within the generalized gradient approximation to density-functional theory. The calculated work function of MgNi-Term $(4.17\mathrm{eV})$ is lower than that of CNi-Term $(5.16\mathrm{eV}\mathrm{}).$ The number of total electrons at the surface layer of MgNi-Term is much decreased, while that of CNi-Term is less decreased than that of MgNi-Term, with respect to their center layers. The number of $\mathrm{Ni}(S)$ d electrons of MgNi-Term is calculated to be 0.08 electrons more than that of CNi-Term. The layer projected l-decomposed local density of states (DOS) show that the difference in the number of $\mathrm{Ni}(S)\ensuremath{-}d$ electrons is due to the strong $\mathrm{C}\ensuremath{-}p$ and $\mathrm{Ni}\ensuremath{-}d$ hybridization at the surface layer of CNi-Term. The peak just below the Fermi level ${(E}_{\mathrm{F}})$ in bulk ${\mathrm{MgCNi}}_{3}$ is broadened substantially at the $\mathrm{Ni}(S)$ of CNi-Term, while that peak survives at $\mathrm{Ni}(S)$ of MgNi-Term. By analyzing the charge density belonging to a very narrow energy window just below ${E}_{\mathrm{F}},$ such considerable modifications of the DOS peak at CNi-Term is seen to be due to the broken local symmetry of the CNi layer at the surface. It is considered that the behavior of the modification of the peak near ${E}_{\mathrm{F}}$ resembles p-band hole doping through C-site substitution, supported by the stability against ferromagnetism determined from total-energy calculations. Superconductivity of the ${\mathrm{MgCNi}}_{3}(001)$ surface is discussed briefly in relation with the modifications of the DOS peak at ${E}_{\mathrm{F}}.$