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GalMOSS performs two-dimensional fitting of galaxy profiles. This Python-based, Torch-powered tool seamlessly enables GPU parallelization and meets the high computational demands of large-scale galaxy surveys. It incorporates widely used profiles such as the Sérsic, Exponential disk, Ferrer, King, Gaussian, and Moffat profiles, and allows for the easy integration of more complex models. Tested on over 8,000 galaxies from the Sloan Digital Sky Survey (SDSS) g-band with a single NVIDIA A100 GPU, GalMOSS completed classical Sérsic profile fitting in about 10 minutes. Benchmark tests show that GalMOSS achieves computational speeds that are significantly faster than those of default implementations.