The proton exchange membrane fuel cell could be made more commercially viable by substituting the expensive platinic catalyst without loss of performance. This should be done simultaneously through optimization and use of a non-precious metal catalyst. In this study, multi-objective optimization of the catalyst layer was done on nonprecious metal catalysts. Nitrogen-doped graphene (NG)-based cobalt was synthesized as a non-precious metal catalyst. Differential equations were solved at the modeling stage by the shooting method, and objective functions were solved at the optimization stage using sequential quadratic programming. NG-based cobalt was evaluated in a cell and then compared with the platinum catalyst. Results present the synthesized non-precious catalyst as an appropriate replacement for existing precious metal catalyst. Also, the polarization curve demonstrates that the current modeling is in good agreement with NG-based cobalt catalyst. Finally, the Pareto curve at the voltage of 0.6 V (and 300 A/m2 current density in the base case) indicated that the best tradeoff between cost and performance of the catalyst layer was achieved when the current density was increased in the range of 5% to 15%.