The implementation of a low-carbon economy is the key to sustainable economic and social development, and low-carbon technological innovation of new energy enterprises is its driving force and core. Based on the establishment of a new energy enterprise low-carbon technology innovation composite system order index system, it integrates synergy theory and genetic algorithms to build a new energy enterprise low-carbon technology innovation composite system(L-CTICS) dynamic co-evolution model, analyze the order and stability of the composite system, select the statistical data of the low-carbon technology innovation composite system of 12 new energy enterprises from 2010 to 2019, establish the corresponding co-evolution model and perform analysis and calculation. The results show that the model can better reflect the dynamic co-evolution relationship of L-CTICS, and detailing the dynamics of the win-win, double-loss and complementary win-loss among the input, output, and support three subsystems in the composite system. The co-evolution relationship fully demonstrates the co-evolution relationship between subsystems and the stability of the overall composite system, and provides a new research direction for low-carbon technology innovation research for new energy enterprises.