The problem of multi-system compatible receiver’s frequency selection is studied based on fixed point theory, and genetic algorithm is applied to resolve the problem. In the frequency space Banach fixed point theory was used to explain the fixed point physical property, which is presented through the evolution of the frequency set in the frequency space. By adequate reciprocal action of the frequency space operator any iterative sequence source frequency set in the frequency space will finally converge to the unique fixed-point object frequency set, the object frequencies of which are the frequency selection problem’s optimal solution. The study of and the solution to the frequency selection problem has been accomplished by a genetic algorithm. Simulation shows that the algorithm can resolve the problem of the multi-system compatible receiver’s frequency selection effectively.