In recent years, tremendous research efforts have been directed toward developing very large floating structures (VLFSs) for the purposes of airports, terminals etc. on the sea to utilize ocean space. There is a VLFS which has a pontoon type structure supported with many dolphins and it is important to investigate sufficiently the behaviors of such VLFS under earthquake loading. The previous paper reported the behaviors of the floating structure, fenders and dolphins obtained from the time history response analyses of the structure with varying the period and velocity of the sinusoidal earthquake wave, when the gaps between the fenders and dolphins were assumed to be zero. This paper reports, succeeding to the previous paper, the results of the time history response analyses of a VLFS supported with 49 dolphins with varying the period and velocity of the applied actual earthquake wave in both cases where gaps between fenders and dolphins are equal to zero and non-zero. In the analyses, the floating structure supported with dolphins is modeled as both a horizontally elastic and rigid plate supported with linear springs and dashpots through gap elements.