The interplay between topological electronic structure and superconductivity has attracted tremendous research interests recently as they could induce topological superconductivity (TSCs) which may be used to realize topological qubits for quantum computation. Among various TSC candidates, superconducting BaSn3 (Tc∼4.4K) has been predicted to be a topological Dirac semimetal (TDS) hosting two pairs of Dirac points along the Γ-A direction. Here, by combining the use of angle-resolved photoemission spectroscopy and ab initio calculations, we identified the predicted topological Dirac fermions and confirmed the TDS nature of the compound. In addition, we observed surface states connecting the Dirac points. Our observations demonstrate BaSn3 as a superconductor with nontrivial topological electronic structures.