To solve the problems of premature convergence and weak ability in global search of the genetic algorithm, a fitness sharing niche genetic algorithm based on extenics is proposed.The algorithm build the matter-element code and extension genetic operator, create niche groups by extension clustering, and preserve the stability of niche groups by combining fitness sharing mechanism and elitist retention strategy. Experiments show that the algorithm can solve the optimal performance with global search ability and fast convergence rate. It is proved to be more effective and accurate than standard geneic algorithm and normal niche genetic algorithm.