The bleed air of an APU engine is heated in an annulus duct of a reverse-flow combustor. The quantity of heat transfer from a combustor section to the bleed air could be analyzed by performance cycle analysis. It was found to be 12.4kW as a result of performance cycle analysis using the test data of GTCP36 APU engine. While it was 6.5kW for same type of the APU engine intended to be designed in this paper. As a result of off-design performance analysis, the total equivalent power of the APU engine was 87.8kW under the condition of ISA, sea level, and 36.5kW under the condition of ISA, 30,000feet, respectively. In order to secure the surge margin bigger than 5%, it can be proposed to maintain 0.022kg/s of bleed air flow in operating condition of maximum shaft power.