Topological crystalline metals/semimetals (TCMs) have stimulated a great research interest, which broaden the classification of topological phases and provide a valuable platform to explore topological superconductivity. Here, we report the discovery of superconductivity and topological features in Pb-intercalated transition-metal dichalcogenide Pb$_{1/3}$TaS$_2$. Systematic measurements indicate that Pb$_{1/3}$TaS$_2$ is a quasi-two-dimensional (q-2D) type-II superconductor ({em T}$_c approx$ 2.8 K) with a significantly enhanced anisotropy of upper critical field ($gamma_{H_{c2}}$ = $H_{c2}^{ab}/H_{c2}^{c}$ $approx$ 17). In addition, first-principles calculations reveal that Pb$_{1/3}$TaS$_2$ hosts multiple topological Dirac fermions in the electronic band structure. We discover four groups of Dirac nodal lines on the $k_z = pi$ plane and two sets of Dirac points on the rotation/screw axes, which are protected by crystalline symmetries and robust against spin-orbit coupling (SOC). Dirac-cone-like surface states emerge on the (001) surface because of band inversion. Our work shows that the TCM candidate Pb$_{1/3}$TaS$_2$ is a promising arena to study the interplay between superconductivity and topological Dirac fermions.
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