As a member of ZrHM (H = Si/Ge/Sn; M = O/S/Se/Te) family materials, which were predicted to be the candidates of topological Dirac nodal-line semimetals, ZrGeSe exhibited particular properties, such as magnetic breakdown effect in the transport measurement, different from its other isostructural compounds, informing an unique topology of the electronic band structure. However, the related experimental research is insufficient until now. Here, we present a systematic study of the band structure and Fermi surfaces (FS) of ZrGeSe by angle-resolved photoemission spectroscopy (ARPES). Our Brillouin zone (BZ) mapping shows multiple Fermi pockets such as the diamond-shaped FS around the zone center Γ point, small electron pocket encircling the X point of the BZ, and lenses-shaped FS in the Γ-M direction. The obtained Fermi velocities and effective masses were up to 9.2 eV·Å and 0.42 me, and revealing an anisotropic electronic property along different high-symmetry k-space directions. Moreover, a kink appears near the Fermi level in the linear Dirac bands along the M-X direction, probably originated from the band hybridization and has not been reported in other ZrHM-type materials. Our findings support that the ZrHM-type material family can be a new platform on which to explore exotic states of quantum matter.