The invention provides a quantum chemistry reaction optimization multi-relay selection method of a cognitive relay network. The method comprises steps of: 1, establishing a cognitive system relay selection model; 2, initializing a quantum molecule set and a system parameter; 3, evaluating the potential energy of all quantum molecules in the set and selecting the measurement state of the quantum molecule with the lowest potential energy as a global optimal solution; 4, arranging the kinetic energy of quantum molecules in a descending order, and performing decomposition reaction, invalid collision, and synthetic reaction; 5, evaluating the potential energy of newly generated quantum molecules, and if the minimum potential energy of the newly generated quantum molecules is less than the minimum potential energy of the previous generation, marking the newly generated quantum molecules as a new global optimal solution; and 6, if the number of iteration times is less than a preset maximum number of iteration times, returning to step 4, otherwise, outputting the global optimal solution. The method balances the primary user constraint condition and non-primary user constraint condition of the cognitive relay network, and chooses a relay selection scheme that maximizes the system throughput based on a quantum chemistry reaction mechanism.