The gold nanoparticles possess novel physical, chemical, and optical properties, which will greatly expand the utility of gold nanoparticles into a wide variety of applications. The growth kinetic of gold nanoparticles at the oil-water interface is a diffusion-controlled process that yields the primary morphological features of dendritic growth. Here, we simulate the growth of two-dimensional gold nanoparticles at the oil-water interface by using a phase field crystal (PFC) method. PFC method describes the evolution of the atomic density of a system with dissipative dynamics driven by the minimization of the free energy functional. By using this, we can simulate the evolution of nano/micro scale structure on the atomic length scale and diffusive time scale. The simulation results show the growth of branches from the core and the generation of narrow gaps between branches. The interesting optical properties of branched gold nanoparticles are also investigated with Finite Difference Time Domain method.