We have performed angle-resolved photoemission spectroscopy on Pb(Bi(1-x)Sb(x))2Te4, which is a member of lead-based ternary tellurides and has been theoretically proposed as a candidate for a new class of three-dimensional topological insulators. In PbBi2Te4, we found a topological surface state with a hexagonally deformed Dirac-cone band dispersion, indicating that this material is a strong topological insulator with a single topological surface state at the Brillouin-zone center. Partial replacement of Bi with Sb causes a marked change in the Dirac carrier concentration, leading to the sign change of Dirac carriers from n type to p type. The Pb(Bi(1-x)Sb(x))2Te4 system with tunable Dirac carriers thus provides a new platform for investigating exotic topological phenomena.