•Humidification dehumidification desalination system powered by a heat-pump.•Mathematical models based on mass and energy balance for combined system.•A closed-air open-water water-heated, and modified air-heated cycles are analyzed.•Maximum GOR of 8.88 were achieved at 80% effectiveness for air heated and water heated cycles.•A maximum GOR greater than 10 can be reached for ideal components. Humidification-dehumidification is a carrier gas based thermal technique that is ideal for small-scale water desalination applications. One advantage of humidification-dehumidification systems is the ability to utilize low grade and renewable energies as heat source to drive the system. This work presents theoretical investigation of humidification-dehumidification desalination system operated by a heat pump. The model is based on the first law of thermodynamics, describing heat and mass transfer in the combined humidification-dehumidification-heat pump cycle. The model predicts the performance of closed-air open-water water-heated, and modified air-heated cycle coupled with a heat pump. To improve the Gain output ratio and energy recovery of the system, a heat pump is used as the source of heating and cooling for the humidification-dehumidification desalination system. Energy rejected in the condenser is used as a source of heat in the humidifier whereas the cooling effect of the evaporator is used to cool incoming seawater for effective condensation of humid air in the dehumidifier. A parametric study is conducted to investigate the influence of system operating parameters, including water and air flowrate, seawater temperature, and refrigerant flow rate on the system performance. Results indicate a maximum Gain output ratio of 8.88 and 7.63 obtained at 80% components effectiveness and mass flow rate ratio of 0.63 and 1.3 for modified air heated and water heated cycle, respectively. A maximum gain output ratio greater than 10 can be achieved for humidifier and dehumidifier effectiveness of 100% leading to more energy efficient systems. The cost of desalinated water production is calculated and the effect of major parameters on its variation is also presented.