Abstract: This paper presents the new learning algorithm for adaptive functional networks loop structures which is designed based on the Banach contraction theorem.This algorithm through levels of thought divides the adaptive functional networks loop structures into multi-storey structure composed of the basic functional networks，then uses algebra algorithm to train all levels of the structure and gets all functional parameters，so as to achieve the overall study.Finally，the simulation results demonstrate that the structure presented has high precision and fast convergence speed.