In previous studies, the effectiveness of the Half-Sweep Geometric Mean (HSGM) iterative method has been shown in solving first and second kind linear Fredholm integral equations using repeated trape­zoidal (RT) discretization scheme. In this work, we investigate the efficiency of the HSGM method to solve dense linear system gener­ated from the discretization of the second kind linear Fredholm in­tegral equations by using repeated Simpson's 1/3(RS1) scheme. The formulation and implementation ofthe proposed method are also pre­sented. In addition, several numerical simulations and computational complexity analysis were also included to verify the efficiency of the proposed method.