Aiming at the deficiency of current system-of-systems effectiveness evaluation methods in the characterization of complex dependencies, the functional dependency network analysis (FDNA) is introduced to evaluate the effectiveness. In view of the basic defects of the existing FDNA methods, based on the utility theory, an improved FDNA method is proposed, which is based on virtual nodes and satisfies the utility constraints, making the structure of the method clearer and the logic more rigorous. Through the case of air defense and anti-missile, the results show that the improved FDNA method has feasibility and effectiveness in the effectiveness evaluation of the system of systems are verified.