This paper presents a new type of circulation system combining heat pump and liquid gap membrane distillation (LGMD) for the concentration of sulfuric acid solution. The proposed hybrid system not only has a simpler flow configuration, but it also demonstrates significant thermal performance advantages. Based on the principle of conservation of mass and energy, a mathematical model is established in Aspen Plus to simulate working conditions. Through varying the relevant parameters, the solution with low boiling point elevation to achieve the maximum water production gain to output ratio (GOR) value was obtained, which is approximately 33 times that of the conventional system under the given condition in this research. Given the temperature difference between the condenser and the evaporator in the heat pump cycle, the higher membrane flux and the maximal value of GOR are obtained at the high feed temperature. However, increasing the molar fraction of the feed solution sharply decreases both the membrane flux and GOR, especially at high feed solution temperatures. Additionally, it was found that the high GOR are obtained when selecting the high boiling point working fluids. Therefore, these results can provide significant references for the further implementation and optimization of the proposed system.