By using angle-resolved photoemission spectroscopy (ARPES) combined with the first-principles electronic structure calculations, we report the quantized states at the surface of a single crystal 2H-TaSe₂. We have observed sub-bands of quantized states at the three-dimensional Brillouin zone center due to a highly dispersive band with light effective mass along k_z direction. The quantized sub-bands shift upward towards E_F while the bulk band at Γ shifts downward with the decrease of temperature across charge density wave (CDW) formation. The band shifts could be intimately related to the CDW. While neither the two-dimensional Fermi-surface nesting nor purely strong electron–phonon coupling can explain the mechanism of CDW in 2H-TaSe₂, our experiment may ignite the interest in understanding the CDW mechanism in this family.