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Mn$_{1-x}$Ga$_x$ (MnGa) with the $L1_0$ structure is a ferromagnetic material with strong perpendicular magneto-crystalline anisotropy. Although MnGa thin films have been successfully grown epitaxially and studied for various spintronics devices, fundamental understandings of its electronic structure are still lacking. To address this issue, we have investigated $L1_0$-MnGa thin films using angle-resolved photoemission spectroscopy (ARPES). We have observed a large Fermi surface with a rhombic shape in the $k_x$-$k_y$ plane overlapping neighboring Fermi surfaces. The $k_z$ dependence of the band structure suggests that the band dispersion observed by ARPES comes from the three-dimensional band structure of MnGa folded by a $\sqrt{2} \times \sqrt{2}$ reconstruction. The band dispersion across the corner of the rhombic Fermi surface forms an electron pocket with a weak $k_z$ dependence. The effective mass and the mobility of the bands crossing the Fermi level near the corner are estimated from the ARPES images. Based on the experimental findings, the relationship between the observed band structure and the spin-dependent properties in MnGa-based heterostructures is discussed.