  Using angle-resolved photoemission spectroscopy (ARPES) and density
functional theory (DFT) we study the electronic structure of layered
BaZnBi$_2$. Our experimental results show no evidence of Dirac states in
BaZnBi$_2$ originated either from the bulk or the surface. The calculated band
structure without spin-orbit interaction shows several linear dispersive band
crossing points throughout the Brillouin zone. However, as soon as the
spin-orbit interaction is turned on, the band crossing points are significantly
gapped out. The experimental observations are in good agreement with our DFT
calculations. These observations suggest that the Dirac fermions in BaZnBi$_2$
are trivial and massive. We also observe experimentally that the electronic
structure of BaZnBi$_2$ comprises of several linear dispersive bands in the
vicinity of Fermi level dispersing to a wider range of binding energy.
