Supercritical carbon dioxide (s-CO2) can be used both as a heat transfer and working fluid in solar power tower plants. The main concern in the design of a direct s-CO2 receiver is the high operating pressures, i.e., close to 20 MPa. At such high pressures, conventional receivers do not exhibit the necessary mechanical strength or thermal performance. In this paper, a receiver based on compact heat exchanger technology is developed. The receiver consists of a group of plates with square-shaped channels which are diffusion bonded together to tolerate the high operating pressure. A computational model is developed and validated against data in the literature. Inconel 625 is used as the base material because of its superior resistance against corrosion in the presence of s-CO2. The receiver heats s-CO2 with mass flow rate of 1 kg/s from 530 °C to 700 °C under a solar flux density of 500 kW/m2. The influence of different parameters on the performance of the receiver is evaluated by a parametric analysis. Subsequently, a multi-objective optimization is performed to determine the optimal geometry of the heat exchanger considering the tradeoff between objective functions, such as unit thermal resistance and pressure drop. The design variables are hydraulic diameter, number of layers, and distance between the channels. The mechanical strength of the system is the constraint to the problem, which is evaluated using an ASME code for the pressure vessels. Finally, the temperature profiles inside the channels and the surface of the receiver are presented. It is shown that the fluid reaches the desired temperature while the maximum temperature of the surface remains well below the material limit.