Point pattern matching (PPM) arises in areas such as pattern recognition, digital video processing and computer vision. In this study, a novel Genetic Algorithm (GA) based method for matching affine-related point sets is described. Most common techniques for solving the PPM problem, consist in determining the correspondence between points localized spatially within two sets and then find the proper transformation parameters, using a set of equations. In this paper, we use this fact that the correspondence and transformation matrices are two unitary polar factors of Grammian matrices. We estimate one of these factors by the GA's population and then evaluate this estimation by computing an error function using another factor. This approach is an easily implemented one and because of using the GA in it, its computational complexity is lower than other known methods. Simulation results on synthetic and real point patterns with varying amount of noise, confirm that the algorithm is very effective.