The quantitative study of combat effectiveness index is crucial for the informatization construction of the armed forces. To solve the problems of limits of quantitative research, low method accuracy, and weak robustness in the study of combat effectiveness index, and to break through the limitations of dominating complex rules, multivariate mathematical models, and strong coupling of influencing factors in the combat effectiveness index function, inspired by the mathematical analysis methods of rules in fuzzy logic theory, we proposed a local approximation based method for fitting combat effectiveness index function. Combining the powerful self-learning and self-deduction capabilities of neural networks, we constructed a corresponding quantitative calculation model based on radial basis function (RBF). Simulation comparative experiments show that the proposed method has an error rate of about 2% and 6% lower than the current best performing method using global approximation, and exhibits stronger robustness. Our method has strong practicality, can be migrated to other military fields, and has good engineering application prospects.