The performance of the traditional turbojet decreases sharply with the increase of the Mach number in the supersonic flight, especially for the turbine-based combined cycle (TBCC) engine in the transition region of the turbojet and scramjet engine. This paper proposes a new high-pressure bleeding-air variable cycle engine (HB-VCE) concept that aims to ease the sharp contradiction between thrust output and fuel consumption of TBCC in the transition region. Through the energy and exergy analyses, the HB-VCE shows greater potential in energy utilization under high Mach flight conditions. The performance of HB-VCE significantly improves as the bleed ratio increases, with a more pronounced effect at higher Mach numbers. At Mach 1.5, the HB-VCE increases the specific thrust (ST) by 2.84 % and reduces the specific fuel consumption (SFC) by 2.73 %. At Mach 2.4, it increases the ST by 6.60 % and reduces the SFC by 6.52 %. Additionally, the controlling law of the critical bleeding ratio constrained by the turbine outlet temperature is proposed. Finally, the effect of the turbine inlet temperature, overall pressure ratio, and Mach number on the critical bleeding ratio is analyzed. This paper provides a promising HB-VCE concept with greater energy utilization for the TBCC design in the transition region.