Abstract: Abstract: The Banach fixed point theorem (Banach’s principle of contraction mapping) is one of the most important theorems in functional analysis. The study of the theorem is quite valuable not only for the pure research but also for the application. In this paper, by analyzing the mathematical essence of the theorem, we extend its contraction condition appropriately. Hence, an extension of the Banach fixed point theorem is proposed and rigorously proved. The scope of the application for the theorem is expanded. The proposed theorem can be used to solve some problems while the Banach fixed point theorem cannot, and then the application of the proposed theorem is given for the powerful evidence.