Spin-orbit coupling (SOC) plays a significant role in the development of topological physics. For example, considering the SOC effect would lead to the formation of a topological insulator with band inversion in a time-reversal symmetry-preserved system and the realization of a Chern phase in a time-reversal symmetry-broken system. Here, by using angle-resolved photoemission spectroscopy combined with first-principles electronic structure calculations, we report SOC-induced ``hidden'' Dirac bands near the Fermi level in the nonsymmorphic topological semimetal InBi. We clearly observe Dirac-like bulk band crossings located at the corner and boundary of the Brillouin zone, providing compelling evidence for three-dimensional Dirac semimetal states. By means of in situ potassium dosing on the crystal surface, we are able to reveal a partial Dirac nodal line along the ${k}_{z}$ direction formed by Dirac fermions close to the Fermi level. Our results not only demonstrate the rich topological states in InBi but also offer a good platform for engineering topologically nontrivial phases.