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 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, the added Stirling mechanism helps achieve its high efficiency and simplicity by utilizing the heat-absorbing ability of liquid air. On one hand, based on Stirling mechanism, gas in the hot space absorbs heat from atmosphere when expanding; gas in the cold space is cooled down by liquid air when compressed. Taking atmosphere as heat source and liquid air as heat sink, a closed Stirling cycle is formed. On the other hand, an exhaust port is set in the hot space. When expanding in the hot space, the vaporized gas is discharged through the exhaust port. Thus, an open cycle is established. To model and analyze the system, the Schmidt theory is modified to describe temperature variation in the cold space, and irreversible characteristic of regenerator is incorporated in the thermodynamic model. The results obtained from the model 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. Its efficiency could be improved by reducing temperature difference between the regenerator and the cold/hot space, increasing the swept volume ratio, decreasing the liquid-gas ratio. To keep outputting work, the leading angle should be set in the region [0, pi]. (C) 2015 Elsevier Ltd. All rights reserved.