With the density functional first-principles calculations, we investigate the structures and electronic properties of transition metal nickel and its (111) surface. The adsorption behavior of single C atom on Ni (111) surface and its co-adsorption with the another C atom on Ni (111) surface are studied. The calculations on band structure and density of states show that significant spin polarization exists at the Fermi level of both nickel and its (111) surface. By comparing the adsorption energy, we find that the hollow site of hexagonal close-packed on the second layer of Ni atoms is the most stable position for the first C atom adsorption, and the hollow site of face-centered cubic on the third layer of Ni atoms is the most stable site for the co-adsorption of second C atom. Charge analysis shows that 1.566e charge transfers from each C atom to the adjacent Ni atom, which is similar to the 1.68e charge transfer in the first C atom adsorption case. The calculations on magnetism show that the magnetic moments of the two C atoms in co-adsorption are 0.059B and 0.060B, respectively, which are larger than the magnetic moment 0.017B of single C atom in Ni (111) surface.