The present paper aims at exploring a hybrid absorption-compression heat pump (HAC-HP) to upgrade and recover the industrial waste heat in the temperature range of 60°C–120°C. The new HAC-HP system proposed has a condenser, an evaporator, and one more solution pump, compared to the conventional HAC-HP system, to allow flexible utilization of energy sources of electricity and waste heat. In the system proposed, the pressure of ammonia-water vapor desorbed in the generator can be elevated by two routes; one is via the compression of compressor while the other is via the condenser, the solution pump, and the evaporator. The results show that more ammonia-water vapor flowing through the compressor leads to a substantial higher energy efficiency due to the higher quality of electricity, however, only a slight change on the system exergy efficiency is noticed. The temperature lift increases with the increasing system recirculation flow ratio, however, the system energy and exergy efficiencies drop towards zero. The suitable operation ranges of HAC-HP are recommended for the waste heat at 60°C, 80°C, 100°C, and 120°C. The recirculation flow ratio should be lower than 9, 6, 5, and 4 respectively for these waste heat, while the temperature lifts are in the range of 9.8°C–27.7 °C, 14.9°C–44.1 °C, 24.4°C–64.1°C, and 40.7°C–85.7°C, respectively, and the system energy efficiency are 0.35–0.93, 0.32–0.90, 0.25–0.85, and 0.14–0.76.