The purpose of this work is to present some existence theorems for coupled fixed points of F-type contractive operator in metric spaces endowed with a directed graph. Our results generalize the main result obtained by Chifu and Petrusel [C. Chifu, G. Petrusel, Fixed Point Theory Appl., 2014 (2014), 13 pages]. We also present applications to some nonlinear integral system equations to support the results.