The surge responses of a semi-submersible under freak wave sequences are studied in time domain. In the present study, a measured New Year Wave sequence is applied to the reference semi-submersible, and its surge responses are analysed to reveal the interaction with freak waves. To investigate the influences of the relative phases, crest amplitudes and the three sister waves, a series of freak wave sequences with different wave parameters have been generated by embedding a freak wave sequence into a random wave sequence. Focuses are paid to the magnitudes of the surge responses, which are directly related to the forces of mooring lines. The surge motion amplitude is observed to be significantly influenced by the freak waves. Main conclusions are drawn regarding the influence of freak waves and their wave parameters on the surge motion responses.