This study presents the optimum design of a ported shroud of a compressor for a hydrogen reciprocating engine of a high-altitude unmanned aerial vehicle. The design aims to expand operating range and improve efficiency by replacing only the casing of the turbo-charger compressor while maintaining the current engine system. Four design variables were selected to determine the slit shape of the ported shroud. Factors, such as efficiency, pressure ratio, and stall mass flow rate at the maximum speed and cruise condition, were defined as objective functions and constraints. A neural network model was constructed, and a multi-point multi-objective optimization design was achieved using a genetic algorithm. k-means clustering was applied to the optimal solutions. Results showed design A with a 4% reduction in stall mass flow rate and design B with a 2% improvement in efficiency under the cruise condition. The performance of each design was confirmed from off-design analysis. The cause of the decrease in stall mass flow rate in design A was investigated by observing flow recirculation from the slit to compressor inlet.