Heat pipes are passive thermal management devices capable of sustaining high heat flux due to heat transport occurring by latent heat of vaporization. They are tube-like devices, made of an evaporator and condenser connected by a wick which consists of multiple grooves. The liquid adheres to these grooves in the condenser section and moves towards the evaporator section because of capillary action in the wick. The structure of the wick geometry is important for the thermal performance of heat pipes. In this work, the steady state heat flux of a grooved heat pipe is improved by employing shape optimization on the grooved wick geometry using a simplified numerical model of the fluid flow and heat transfer within the wick. In order to facilitate gradient based shape optimization it is crucial to employ a precise and robust though fast method for performance prediction. The model is based on assumptions similar to those in [1] and [2]. The heat pipe is modeled assuming liquid in the grooved wick, vapor in the vapor cavity and thermal conduction in the outer wall and fins between grooves. The fluid phases are coupled through a circular meniscus along the entire groove length with mass flux and pressure boundary conditions. The fluid flows and heat problem are weakly coupled through the evaporation and condensation across the meniscus. The shape parametrization entails varying the width of a singular groove along the length of the grooved wick. The goal is to create a more efficient heat pipe capable of maintaining a higher steady-state heat flux. The optimized wick structure improves the performance of the heat pipe by 30% compared to a heat pipe with a straight grooved wick without increasing the occupied space, similar to [3].