The surface premelting, melting behavior, melting competition, and structural transition of shell-closed icosahedral ICO and cuboctahedral CUB nickel clusters with atoms from 309 to 2057 were discussed extensively by using quantitative caloric curves based on the modified analytic embedded atom method and molecular dynamics, qualitative three-dimensional structural visualization of symmetric truncation, and the radial number distribution function. These studies reveal that smaller clusters melt at lower temperatures and a solid-to-solid structural transition occurs from CUB to ICO structure during melting process. The shell-closed ICO clusters could only be preferred until 923 atoms at temperatures no higher than 1380 K, which is in agreement with the experiments. The melting temperature of larger clusters would depend on their starting structures, which can be attributed to surface premelting.