Using angle-resolved photoemission spectroscopy and density functional theory (DFT) we study the electronic structure of layered BaZnBi2. Our experimental results show no evidence of Dirac states in BaZnBi2 originated either from the bulk or the surface. The calculated band structure without spin-orbit interaction shows linear band dispersions at X along the X-M high-symmetry line. In addition, the calculations suggest a gapless band crossing point along the Γ-M high-symmetry line. However, as soon as the spin-orbit interaction is turned on, the band crossing point is significantly gapped out. These observations suggest that the Dirac fermions in BaZnBi2 are trivial similar to the Dirac states observed in grapheme. The experimental observations are in good agreement with the DFT calculations.