An unconventional Stirling engine is proposed and its theoretical analysis is performed. The engine belongs to a "cryogenic heat engine" that is fueled by cryogenic medium. Conventional "cryogenic heat engine" employs liquid air as a pressure source, but disregards its heat-absorbing ability. Therefore, its efficiency can only be improved by increasing vapor pressure, accordingly increasing the demand on pressure resistance and sealing. In the proposed engine, a closed cycle structure of Stirling engine is added to combine with the open cycle structure of a conventional cryogenic heat engine to achieve high efficiency and simplicity by utilizing the heat-absorbing ability of liquid air. Besides, the theoretical analysis of the proposed engine is performed. The Schmidt theory is modified to model temperature variation in the cold space of the engine, and irreversible characteristic of regenerator is incorporated in the thermodynamic model. The modeling results show that under the same working pressure, the efficiency of the proposed engine is potentially higher than that of conventional ones and to achieve the same efficiency, the working pressure could be lower with the new mechanism. Composition of exergy loss in the proposed engine is analyzed. (C) 2015 Elsevier Ltd. All rights reserved.