There are some difficulties in researches on supervised learning using fuzzy rule-based systems: difficulty of the selection of effective input variables and difficulty of the decision of proper number of rules. In this paper, GAd (Genetic Algorithm with Degeneration) is used to optimize the structure of RBF (Radial Basis Function) fuzzy rule bases. GAd employs real-coded genetic algorithms and introduces the idea of genetic damage. In GAd, the information of damaged rates is added to each gene. GAd inactivates the genes that have lower effectiveness using genetic damage, realizes degeneration and reduces unnecessary variables and rules. It is shown that GAd is an efficient algorithm for the structural learning of RBF fuzzy rule-based systems by applying GAd to learning of some function identification problems.