There is tremendous surplus heat in flue gas from gas boilers which cannot be efficiently recovered by conventional condensing heat exchangers. As one of heat recovery systems, boilers equipped with vapor pump system (BEVP system) is complicated. To improve system performance, theoretical investigation and mathematical models are required. However, these are not proposed in previous work. In this study, thermodynamic work principles and moisture loop of BEVP system are analyzed. It utilizes the 'constant vapor flux' property of natural gas combustion and the humidity level of combustion generated vapor flux depends on the humidity level of combustion air. The system is divided into two subsystems for better understanding. Subsystem I is used for dehumidification, and subsystem II is for total heat recovery, serving as a 'vapor pump'. The core optimization principle of BEVP system is to decrease the moisture transfer driven force of vapor pump, which is used for total heat recovery in Subsystem II. A mathematical model is established to quantitatively characterize the BEVP system. Analytical solutions are derived with clear physical significances and additivity property. The mathematical model is used to conduct performance analyses under various conditions. The systematic feasible domain is developed with iso-efficiency lines. (C) 2019 Elsevier Ltd. All rights reserved.