Intense seismic excitations might be considered as one of the most important loading cases imposed on offshore jacket platforms. To perform seismic assessments for these structures, appropriate suites of ground motions can be selected by different methodologies. Since time history analyses of fixed offshore platforms are truly time consuming, number of selected records can considerably change the computational expenses. This paper quantitatively investigates the effects of sample size of records on seismic performance of these structures. Thus, several record suites with different sample sizes are selected from a target population with 40 records so that the differences between the logarithmic mean and standard deviation of their response spectra become minimum using Genetic Algorithm. The results show that the fragility curves based on the suites with larger sample sizes are closer to the target fragility. Nevertheless, according to the results of the investigated case study, some suites with smaller sample sizes (e.g. 20 or 25) could lead to relatively acceptable accuracy at almost half the computational expenses. Also, the correlation coefficients between the collapse fragilities of the selected record sets and the target one are very close to unity, indicating that these collapse fragilities are linearly correlated with the target one.