In this article, thermodynamic modeling of a cogeneration system consisting of a series two-stage organic Rankine cycle (STORC) and a proton exchange membrane (PEM) fuel cell is conducted. The fuel cell dissipated heat is utilized as STORC plant input. In order to gain a higher efficiency for the proposed cogeneration system, the condenser of the organic Rankin cycle is replaced by a thermoelectric generator (TEG) to minimize heat loss. Moreover, zeotropic mixtures have been employed due to their lower irreversibility compared to single working fluid. Simulation code is developed in MATLAB software linked with the REFPROP software to extract the thermodynamic properties. This simulation code calculates the exergy efficiency and system's total cost rate. Since the performance of the system is affected by the working fluid, three zeotropic mixtures are compared with R123. The parametric study shows that high pressure (HP) and low pressure (LP) evaporator temperature, current density, and PEM operating pressure significantly affect the total cost rate and the second law efficiency. The results indicate that Ipentane-cis Butane has better efficiency among the selected zeotropic mixtures. Furthermore, the genetic algorithm multi-objective optimization is applied to determine the optimal design parameters of the system in a scatter distribution schematic. Finally, the normalized Pareto frontier of Ipentane-cis Butane is given and the related best point of working as a higher exergy efficiency and lower cost rate are specified. Eventually, it is concluded that the integration of STORC with primary PEM fuel cell improves overall exergy efficiency by 1.9%. The total cost rate for optimum point can be in a range of 1.36-14.94 ($/h), depending on the hydrogen production process. (c) 2021 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.