Despite the advantages of flywheel energy storage, including low cost, a long life-cycle, and high reliability, the flywheel hybrid vehicle (FHV) has not yet been mass-produced because it usually uses two transmissions, one for the engine and the other for the flywheel, which leads to cost, packaging, and complexity concerns. In this paper, a novel power-split flywheel hybrid powertrain (PS-FHV) that uses only one transmission is proposed to mitigate these issues. The proposed PS-FHV includes one continuously variable transmission (CVT) and three planetary gear-sets integrated with a flywheel, to provide full hybrid functionality at any speed, which leads to high fuel economy and fast acceleration performance. To prove and verify the PS-FHV operation, the system was modeled and analyzed using a lever analogy to demonstrate that the system is capable of performing power distribution and regulation control, which are required for hybrid driving modes. Using the derived model, PS-FHV driving was simulated to assess the feasibility of the proposed system and estimate its performance. The simulation results confirm that the PS-FHV is a feasible system and that, compared to hybrid electric vehicles (HEVs), it provides comparable fuel economy and better acceleration performance.