The authors predicted that $Co_2HfSi$, a $Co_2$-based full Heusler alloy, is being a half-metallic ferromagnet by first-principles calculations using the all electron full-potential linearized augmented plane wave method which adopts the generalized gradient approximation. The integer value of the calculated total magnetic moment of 2.00 ${mu}_B$ per formula unit and a spin gap of 0.69 eV in spin down state confirmed the half-metallicity of bulk $Co_2HfSi$. For the $Co_2HfSi$(001) surface, we considered two possible surface terminations, namely, Co terminated and HfSi terminated surfaces. It was found that half-metallicity was retained at the HfSi-terminated surface but not at the Co-terminated surface. The magnetic moment of surface Co atoms in the Co-terminated surface was slightly lower than that of Co atoms in deep inner-layers, whereas the magnetic moments of Hf and Si atoms at the HfSi-terminated surface were almost same as those in deep inner-layers.