Supercritical organic Rankine cycle (SORC) is an improved ORC architecture with lower exergy destruction and better heat source utilization when compared with a subcritical one. The accurate design of its vapor generator is of critical importance due to the fact that heat transfer performance significantly affects thermal efficiency, power output, and size of the overall system. This paper aims to develop a mathematical model of the SORC vapor generator using plate-fin heat exchanger. The finite volume method is applied to deal with the properties' variation problem of the supercritical fluids. Multi-objective optimization is employed by the nondominated sorting genetic algorithm II to find the optimum geometry design. The objective functions are the number of entropy production units, annual cost, and volume. For a specific SORC system, an optimum vapor generator is designed using the developed model. Parametric studies are conducted to assess the effect of geometry parameters on the vapor generator performance. The off-design performance of the vapor generator is also evaluated under different mass flow rates and different heat source inlet temperature conditions.