Temperature limits of composite material combustor significantly restricts the hydrogen-fueled scramjet engine performance in a wide range of Mach number flight. In order to solve this problem and conserve fuel, constant static-temperature heating has been newly proposed, which means that the static temperature keeps constant during combustion process of the engine. A thermodynamic cycle including constant static-temperature heating and a compound cycle model are developed corresponding to variable and constant inlet pressure ratios, respectively. Thermodynamic cycle analysis is carried out to evaluate the performance of a scramjet engine at different flight conditions and fuel equivalence ratios. Compared with traditional scramjet cycle, it finds that the two kinds of thermodynamic cycles with constant static-temperature heating can significantly improve the efficiency of the engine and provide greater thrust without over-temperature of combustor. Moreover, to maintain the constant static temperature heating in the scramjet, the area expansion requirements of combustor is also presented via some equations. Copyright (C) 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.