The Environmental Control System (ECS) is the largest consumer of non-propulsive energy, accounting for 3-5% of total power consumption. This significant energy demand necessitates the investigation of new ECS architectures, seeking more efficient solutions. A novel electrically driven ECS is presented that combines features of the Air Cycle Machine and Vapor Compression Cycle. The system design is optimized to minimize weight and power consumption for a critical operating condition, i.e., the aircraft is on the ground during a hot and humid day. The optimization framework integrates the thermodynamic cycle, component sizing and detailed high-speed centrifugal compressor design for the refrigerant. A steady-state model of the ECS has been developed using the acausal language Modelica acausal modelling language, and the optimization framework relies on a Python-Modelica interface. The outcome of the simulation proves that the design of a hybrid ECS is feasible. The results show a trade-off between system efficiency and weight. An optimal system design has been identified to minimize the specific fuel consumption for a typical flight mission of single-aisle aircraft, accounting for the power consumption at ground conditions and the weight of the heat exchangers. The selected design is then used to verify the system performance in off-design during standard cruise operating conditions.