Based on the outcomes of scientific research on ELSP, the authors put forward a mathematic model to solve Single-machine Economic Lot sizes Scheduling Problem under capability contraints. For ELSP is a NP hardness, we solve the problem with GA (Genetic algorithm) according to the charictistics of the model and achieve the numerical results by phi. The results indicate that our results are better than literature. At the same time our results approach the results under no capability contraints that sufficiently prove the validity of our algorithm.