  The search of new topological phases of matter is one of the new directions
in condensed matter physics. Recent experimental realizations of Dirac
semimetal phases pave the way to look for other exotic phases of matter in real
materials. Here we present a systematic angle-resolved photoemission
spectroscopy (ARPES) study of NdSb, a potential candidate for hosting a Dirac
semi-metal phase. Our studies reveal two hole-like Fermi surface pockets
present at the zone center ($\Gamma$) point as well as two elliptical
electron-pockets present in the zone corner (X) point of the Brillouin zone
(BZ). Interestingly, Dirac-like linearly dispersive states are observed about
the zone corner (X) point in NdSb. Our first principles calculations agree with
the experimentally observed bands at the $\Gamma$ point. Moreover, the
Dirac-like state observed in NdSb may be a novel correlated state, not yet
predicted in calculations. Our study opens a new direction to look for Dirac
semi-metal states in other members of the rare earth monopnictide family.
