Dropwise condensation (DWC) is a ubiquitous phenomenon of great importance to several engineering processes due to its higher heat and mass transfer rates when compared with film condensation. Droplet condensation on a surface with wettability gradient is a complex phase change process, as the droplet self-propels toward the high surface energy region with a moving contact line and variable advancing and receding contact angles during the growth process. Approaches to model the system are usually taken by allowing the flow to slip near the phase interface or to use adsorption and desorption relations from molecular theory near the contact line. These approaches end up modifying and imposing ad-hoc relations to the value of the static contact angle. However, a static contact angle is known to be incompatible with a moving contact line when large variations in advancing and receding angles are expected. An energetic prescription of the contact angle model is expected to provide a physically consistent framework for numerical simulations of moving boundary problems. In this work, we simulate the condensation of a two-dimensional sessile droplet in its own vapor on a surface with a wettability gradient. The condensation process is modeled by the Navier-Stokes-Korteweg model enclosed with the van der Waals equation of state. The contact angle is modeled through a constitutive equation based on a wall-interaction energy for diffuse-interface models. The results show that a wettability gradient influences condensation rate near the moving contact line.