Generation temperatures from 110 °C to 140 °C are not enough to drive a double effect LiBr-water absorption cycle but too high for a single effect cycle under typical operating conditions. A novel LiBr-water absorption cycle which contains an AGX (absorber generator heat exchanger) is introduced for this. The AGX absorption cycle is able to make use of the high pressure condensation heats of different temperature, and get different amounts of extra refrigeration thus obtains 1.n effect refrigeration. The novel cycle can work under generation temperatures from 85 °C to 150 °C with evaporation temperature of 5 °C, absorption temperature of 35 °C and condensation temperature of 40 °C. The results of simulation show that the novel cycle can work in single effect mode, 1.n effect mode and double effect mode when the generation temperatures are in the ranges of 85 °C–93 °C, 93oC–140 °C and 140 °C–150 °C, and reach a COP (coefficient of performance) of 0.75, 0.75–1.08 and 1.08–1.25 respectively. Comparison between this novel cycle and existing cycle working under similar generation temperature range shows that the novel cycle has a better performance. The large working range also makes the cycle suitable for solar cooling utilizing medium temperature solar collector.