In today’s world, using of biogas is increasing due to its methane content, renewability, and low price. Solid oxide fuel cell is one of the best energy conversion technologies, in order to use biogas and it has a high potential to integrate with the gas turbine. In this paper, solid oxide fuel cell-gas turbine hybrid system, which is fed by biogas is modeled with respect to energy and economic aspects. Maximization of electrical energy efficiency and minimization of total investment cost are objective functions, which are considered to find the optimal design variables of the hybrid system. First, each component of the hybrid system is modeled and validated individually. Then, in order to optimize the hybrid system, multi objective optimization via NSGAII is implemented and optimal values of design parameters of the hybrid system were calculated. Optimal point is obtained using Euclidian non-dimensionalization and LINMAP decision making method in Pareto front. So, optimal design values are 66 percent and 175227.4 $, which are electrical energy efficiency and total investment cost, respectively. In optimal point Levelized unit cost is 6.3 cent per kWh. Finally, in order to determine the effect of design parameters on the objective functions, sensitivity of each design parameters were analyzed using Sobol's sensitivity analysis method. Results show that compressor pressure ratio has the maximum effect on electrical energy efficiency. Furthermore, turbine isentropic efficiency and fuel cell current have the maximum effect on the total investment cost.