Single-phase 25kV AC traction power supply system (TPSS) is widely used for electric power feeders in high-speed rail. Modern locomotives draw a large amount of unbalanced, inductive power from two phases of the grid through the traction transformer and lead to severe problems of voltage unbalance and reactive power existence. These problems are mitigated in the promising co-phase TPSS with the equipment of Railway Power Conditioner (RPC) or Hybrid Power Quality Conditioner (HPQC), in which HPQC can operate with a lower voltage and cost. However, HPQC installation involves the adoption of a bulky and expensive coupling transformer. In this paper, a co-phase TPSS employing asymmetric back-to-back modular multilevel converter (MMC) is proposed and it is named asymmetric three-leg hybrid HPQC (ATHPQC). Through the simulation verifications in this research work, the proposed design can effectively remove the additional and costly step-down coupling transformer, which is required by symmetric HPQC. For comprehensiveness of the ATHPQC design, internal circulating current modeling and analysis are investigated. Control system is implemented, including external compensating current control, internal balancing control and PWM module. ATHPQC is a promising alternative TPSS for next-generation high-speed rail.