This paper investigates the application of the 2-Point Half-Sweep Block Arithmetic Mean (2-HSBLAM) iterative method with first order composite closed Newton-Cotes quadrature scheme for solving first kind linear Fredholm integral equations. The formulation and implementation of the method are presented. In addition, numerical results of test problems are also included to verify the performance of the method compared to existing Arithmetic Mean (AM) and 2-Point Full-Sweep Block Arithmetic Mean (2-FSBLAM) methods. From the numerical results, it is noticeable that the 2-HSBLAM method is superior than AM and 2-FSBLAM methods in terms of computational time. © 2013 AIP Publishing LLC.