Mesh-free particle methods are increasingly being used instead of grid based numerical methods in many engineering applications, including free-surface fluid flows. Smoothed Particle Hydrodynamics (SPH) method is one such meshless, Lagrangian particle method utilized for modeling large deformations or flows with free surfaces. In SPH, the problem domain is discretized into particles without any connectivity and physical quantities of the flow are obtained by tracing the motion of particles. SPH was originally developed for compressible flow and has later been improved to satisfy the incompressible condition by various authors. In typical incompressible smoothed particle hydrodynamics (ISPH) formulations, a semi-implicit integration scheme is applied to particle discretized equations to solve incompressible flow problems. This requires solving linear equations, which takes up a lot of device memory, thus limiting the possibility of carrying out large scale problems. This study explains the application of a fully-explicit time integration scheme for fluid simulations using the ISPH method. In addition, we used a GPU environment for the computer simulations through an authorial program written in CUDA Fortran. Thus, the purposes were to avoid the need of solving linear equations, therefore reducing memory usage and to utilize the parallel processing power of GPU to accelerate the code. On the other hand, GPU is more widely available compared to supercomputer CPUs, which is the generally used environment for ISPH calculations. Dam-break simulations and validation tests were conducted to validate the proposed SPH method. With the proposed method and computational environment, the calculation speed was increased and memory usage was decreased significantly and large fluid simulations could be carried out. Thus, the proposed method and improvements could pave way in simulating large-scale problems, such as tsunami run-up analyses and other natural disaster simulations.