The hybrid electric propulsion system presents significant potential and advantages for the advancement of general electric aviation. Efforts to optimize the parameters of the serial hybrid electric propulsion (S-HEP) system can effectively enhance energy utilization efficiency. This paper proposes an integrated analysis method to address the matching design problem specific to the S-HEP system, tailored for fixed-wing Vertical Take-off and Landing (VTOL) aircraft. The method combines the performance requirements of the flight profile with the constraints of the S-HEP system. To expedite the computation process, thrust and power demands are modelled as sectionally functional curves, which align with the matching design and parameter identification of the propulsion system, generator set, and batteries. To ensure relevance to actual conditions, several empirical equations are derived from available test data. A case study of an S-HEP system for a 100 kg fixed-wing VTOL aircraft is conducted to verify the proposed method. Systematic simulations demonstrate that the design of the S-HEP system can fully satisfy the thrust and power requirements of the aircraft, providing highly efficient and energy-saving operational performance. With 3.4 kg of fuel, the flight time of the 100 kg fixed-wing VTOL aircraft can exceed one hour. In comparison to pure internal combustion engines, fuel consumption has been reduced 11.7%, illustrating that the proposed method provides a normative approach for hybrid electric propulsion.