Symmetries analysis and gauge modeling of systems extend the gauge field theory from physics into economic systems,biological systems and social systems in order to solve the most fundamental problems in systems science such as how to describe the interaction between any two elements.On the core issue of finding invariants in gauge modeling of commodity market economic system,from the perspective of economic significance,the primary facts in commodity economy and fundamental properties of commodities revealed by GDP were analyzed,and then three kinds of symmetries of GDP with respect to money were clarified,and at the mathematical level,the transformation groups corresponding to the symmetries were presented,which reveals that GDP is an invariant in the movement of commodity economic system.