The fabrication of porous metallic composite coating on the heating surface to improve pool boiling heat transfer (BHT) performance has received significant attention in recent years. In this work, Cu–GNPs nanocomposite coatings, which were prepared on a copper substrate using various current densities through a two-step electrodeposition technique, were used as heating surfaces to study the pool BHT performance of refrigerant R-134a. The surface morphology, elemental composition, thickness, surface roughness, and porosity of prepared Cu–GNPs nanocomposite coatings are studied and presented in detail. All Cu–GNPs nanocomposite coated surfaces exhibited improved boiling performance compared to the plain Cu surface. The heat transfer coefficient (HTC) values for Cu–GNPs nanocomposite coated Cu surfaces prepared at 0.1, 0.2, 0.3, and 0.4 A/cm2 were improved up to 1.48, 1.67, 1.82, and 1.97, respectively, compared with the plain Cu surface. The enhancement in the HTC is mainly associated with the increase in surface roughness, active nucleation site density, and micro/nanoporosity of the heating surface.