Apart from electricity, high-temperature proton exchange membrane fuel cell also produces a lot of waste heat, leading to energy wasting. Harvesting the waste heat for additional cooling production may further improve the commercial competitiveness. In this paper, we propose a novel combined system model that integrates high-temperature proton exchange fuel cell with heat-driven elastocaloric cooling system. Considering different sources of irreversible effects, mathematical formulas of performance indicators for each subsystem and combined system are specified. In addition, energetic and exergetic analyses are conducted to assess the potentiality of elastocaloric cooling system as a waste heat recovery candidate. The maximum power output density of the combined system can be boosted by 9.18% in comparison with that of a single fuel cell. The basic performance features and optimum criteria of the proposed system performance are expounded. Extensive sensitivity analyses and calculation examples have been conducted to check the dependance of the proposed combined system performance on some important design variables and operation conditions.