  The signatures of topological superconductivity (TSC) in the superconducting
materials with topological nontrivial states prompt intensive researches
recently. Utilizing high-resolution angle-resolved photoemission spectroscopy
and first-principles calculations, we demonstrate multiple Dirac fermions and
surface states in superconductor BaSn$_3$ with a critical transition
temperature of about 4.4 K. We predict and then unveil the existence of two
pairs of type-\uppercase\expandafter{\romannumeral1} topological Dirac fermions
residing on the rotational axis. Type-\uppercase\expandafter{\romannumeral2}
Dirac fermions protected by screw axis are confirmed in the same compound.
Further calculation for the spin helical texture of the observed surface states
originating from the Dirac fermions give an opportunity for realization of TSC
in one single material. Hosting multiple Dirac fermions and topological surface
states, the intrinsic superconductor BaSn$_3$ is expected to be a new platform
for further investigation of the topological quantum materials as well as TSC.
