The requirement of simultaneous heating and cooling effects at different zones of a building demands for the development of an energy-efficient air-conditioning system for heating and cooling outputs. In order to fulfil this requirement, a novel multistage hydrogen-alloy-based sorption heat pump (H-A SHP) for space air-conditioning is proposed in the present work. The proposed system produces multiple cooling and heating outputs at 20 degrees C and 45 degrees C, respectively, with single heat input at 160 degrees C. A set of MmNi(5), La0.8Ce0.2Ni5, MmNi(4.4)Al(0.6), and LaNi4.6Al0.4 metal hydrides (MHs) is chosen to operate at the above-mentioned temperature range with hydrogen as working fluid. The proposed system can completely eliminate the requirement of conventional compressor because it operates using waste heat, and useful outputs (cooling-heating) result from reaction enthalpies (MH + H-2 interaction). The thermodynamic and heat-hydrogen transfer analyses of H-A SHP are carried out through finite volume approach, in which heat and mass transfer equations are solved to foresee the variations in MH bed temperature, hydrogen concentration, and heat interactions during cycle operation as well as the amount of cooling and heating outputs delivered to the air-conditioning space. The numerical code is validated with experimental pressure-concentration isotherms (PCIs) measured through Sievert's apparatus. The maximum heat exchange during the cooling and heating processes, at a particular instant of time, is observed as 257.5 and 286.1 W with cooling temperature of 10 degrees C and heating temperature of 53 degrees C, respectively. The thermodynamic performance is estimated as 178.5 kJ of cooling effect, 265.5 kJ of upgraded heat with overall coefficient of performance (COP) of 6.8, and overall specific alloy output of 396.5 W/0.34 kg of alloy.