Automated backbone resonance assignment is very challenging because NMR experimental data from different experiments often contain errors. We developed a method, called GANA, which uses a genetic algorithm to perform backbone resonance assignment with high precision and recall. GANA takes spin systems as input data, and assigns spin systems to each amino acid of a target protein. We use the BMRB dataset (901 proteins) to test the performance of GANA. We also generate four datasets from the BMRB dataset to simulate data errors of false positive, false negative, linking error, and a mixture of the above three cases to examine the fault tolerance of our method. The average precision and recall rates of GANA on BMRB and the four simulated test cases are above 95%. Furthermore, we test GANA on two real wet-lab datasets: hbSBD and hbLBD. The precision and recall rates of GANA on these two datasets are 95.12% and 92.86% for hbSBD and 100% and 97.40% for hbLBD.