•Cost-emission performance of PV/battery/fuel cell hybrid energy system is studied.•Multi-objective optimization model for cost-emission performance is proposed.•ε-constraint method is proposed to produce Pareto solutions of multi-objective model.•Fuzzy satisfying approach selected the best optimal solution from Pareto solutions.•Demand response program is proposed to reduce both cost and emission. Optimal operation of hybrid energy systems is a big challenge in power systems. Nowadays, in addition to the optimum performance of energy systems, their pollution issue has been a hot topic between researchers. In this paper, a multi-objective model is proposed for economic and environmental operation of a battery/fuel cell/photovoltaic (PV) hybrid energy system in the presence of demand response program (DRP). In the proposed paper, the first objective function is minimization of total cost of hybrid energy system. The second objective function is minimization of total CO2 emission which is in conflict with the first objective function. So, a multi-objective optimization model is presented to model the hybrid system’s optimal and environmental performance problem with considering DRP. The proposed multi-objective model is solved by ε-constraint method and then fuzzy satisfying technique is employed to select the best possible solution. Also, positive effects of DRP on the economic and environmental performance of hybrid system are analyzed. A mixed-integer linear program is used to simulate the proposed model and the obtained results are compared with weighted sum approach to show the effectiveness of proposed method.