Thermally driven absorption heat pump is regarded as one of the most promising methods to efficiently utilize low-grade heat, reduce energy consumption and greenhouse gas emissions. However, there are still limitations when using it at low ambient temperature in cold regions, and its application is limited by their low system performance. In this study, we proposed a novel Generator-absorber heat exchange (GAX) based NH3/H2O cross-type absorption-resorption heat pump driven by waste flue gas, which amalgamates the absorption-resorption and GAX cycles, yielding a dual advantage of diminished heat source temperature and operating pressure requirements. Additionally, it substantively enhances the system's performance by capitalizing on the cross-type solution cycle integration. A mathematical model has been developed and the results have been compared and validated with those reported in the literature. The proposed system is comprehensively studied from the view of energy, exergy, economic and environmental (4E) analysis to determine its advantages and disadvantages. The results reveal that the proposed system achieves a maximum COP of 2.742 under specific operating conditions, which is 82.8% higher than the conventional absorption heat pump (AHP), and 30.57% higher than the conventional GAX-AHP. Besides, the addition of a compressor can significantly enhance the performance of the system at lower driving heat source temperatures. At a PH/PL pair of 1.7/0.47 MPa, the static payback period is 4.113 years, with the heating capacity of 88.51 kW and the supply water temperature of 54.6 °C, showcasing favorable system performance. Furthermore, the total atmospheric pollutant emissions could be reduced by 30,998 kg/year compared to the conventional heating method.