An optimized acoustic metamaterial (OAM) railway sound barrier has been designed to address the growing noise problem in railway construction. The low-frequency broadband noise attenuation is realized by an reverse design method relying on genetic algorithm-neural network (GA-NN). Simulation results show that the OAM can perfectly cover the target frequency band from 400 Hz to 1000 Hz with a bandgap ranging from 210 Hz to 1253 Hz. Compared with the initial acoustic metamaterial (IAM), the bandgap of the OAM is widened by 1295 Hz, and the sound transmission loss is improved by 15 dB. The noise reduction performance of the OAM is verified by the experiments of the fully-enclosed impedance tube and the simulation of the acoustic field modes. The acoustic experiments of the semi-enclosed OAM sound barriers show that the noise reduction of OAM sound barriers has a low-frequency broadband noise reduction effect. Compared with the existing sound barriers, the average noise reductions of OAM sound barriers in the target frequency band and bandgap range are improved to 15.9 dB and 7.8 dB, respectively.