A quasi-two-dimensional electron system resulting from a layered crystal structure is a common feature of high-temperature superconductors. In such a system, an interlayer Josephson coupling is responsible for bulk superconductivity. However, materials of interest are limited for Bi-based cuprates which have underdamped and systematically controllable interlayer Josephson junctions. Here, we report the c-axis transport properties and an interlayer Josephson coupling of a 1212-type cuprate superconductor which have not been well studied so far. We demonstrate an underdamped Josephson coupling between superconducting CuO₂ double-layers through a chemically controllable (Pb,Cu)–O barrier layer. Broadly tunable Josephson properties through a chemical substitution demonstrated in this work in conjunction with a rich variety of barrier layers for 1212-type cuprates can potentially offer a material breakthrough in the research field of intrinsic Josephson junctions.