We present the application of a machine learning based galaxy group finder to real observational data from the Sloan Digital Sky Survey Data Release 13 (SDSS DR13). Originally designed and validated using simulated galaxy surveys in redshift space, our method utilizes deep neural networks to recognize galaxy groups and assess their respective halo masses. The model comprises three components: a central galaxy identifier, a group mass estimator, and an iterative group finder. Using mock catalogs from the Millennium Simulation, our model attains above 90% completeness and purity for groups covering a wide range of halo masses from ∼1011 to ∼1015 h−1M⊙. When applied to SDSS DR13, it successfully identifies over 420,000 galaxy groups, displaying a strong agreement in group abundance, redshift distribution, and halo mass distribution with conventional techniques. The precision in identifying member galaxies is also notably high, with more than 80% of groups with lower mass achieving perfect alignments. The model shows strong performance across different magnitude thresholds, making retraining unnecessary. These results confirm the efficiency and adaptability of our methodology, offering a scalable and accurate solution for upcoming large-scale galaxy surveys and studies of cosmological formations. Our SDSS group catalog and the essential observable properties of galaxies are available at https://github.com/JuntaoMa/SDSS-DR13-group-catalog.git.