The lowest-energy structures and properties of neutral nickel clusters Nin(n=31-35)were studied by a combination method of genetic algorithm(GA)searching with a tight-binding potential and the density functional theory(DFT)calculations.Structural candidates obtained from our GA search were further optimized with first-principles calculations.Four typical isomers of lower-energy neutral Nin(n=31-35)clusters were shown,as well as their binding energies per atom(Eb),second differences in energy and magnetic moment.The medium-sized nickel clusters in a size range from 31 atoms to 35 atoms were found to favor the distorted double-icosahedron-like structures.The fragments composed of the central atoms appear as some small stable clusters.