Considering energy conversion efficiency, pollution emissions, and economic benefits, combining biomass with fossil fuels in power generation facilities is a viable approach to address prevailing energy deficits and environmental challenges. This research aimed to investigate the thermodynamic and exergoeconomic performance of a novel power and cooling cogeneration system based on a natural gas−biomass dual fuel gas turbine (DFGT). In this system, a steam Rankine cycle (SRC), a single-effect absorption chiller (SEAC), and an organic Rankine cycle (ORC) are employed as bottoming cycles for the waste heat cascade utilization of the DFGT. The effects of main operating parameters on the performance criteria are examined, and multi-objective optimization is accomplished with a genetic algorithm using exergy efficiency and the sum unit cost of the product (SUCP) as the objective functions. The results demonstrate the higher energy utilization efficiency of the proposed system with the thermal and exergy efficiencies of 75.69% and 41.76%, respectively, while the SUCP is 13.37 $/GJ. The exergy analysis reveals that the combustion chamber takes the largest proportion of the exergy destruction rate. The parametric analysis shows that the thermal and exergy efficiencies, as well as the SUCP, rise with the increase in the gas turbine inlet temperature or with the decrease in the preheated air temperature. Higher exergy efficiency and lower SUCP could be obtained by increasing the SRC turbine inlet pressure or decreasing the SRC condensation temperature. Finally, optimization results indicate that the system with an optimum solution yields 0.3% higher exergy efficiency and 2.8% lower SUCP compared with the base case.