The non-linear behavior of ice-induced vibration of an offshore platform with four legs is investigated in this paper. The equations of motion of the system are derived by using the Hamiltonian Principle The force of moving ice based on the self-excitation and locking is used to model the phenomenon of contact between the ice and the platform. By using the approach of multiple scales, the primary resonance of the ice-induced vibration of the platform is analyzed. The numerical results show that there exist several kinds of combination resonances, including self-excited vibration and locking vibration. These results coincide with those observed from an offshore platform in the North China Sea, and hence enable one to gain insight into the ice-induced vibration of offshore platforms.