A cuprate superconductor containing double mercury layers was synthesized with a high-pressure, high-temperature technique. The compound, with chemical formula Hg2Ba2Y1-xCaxCu2O(8-delta), contains a double HgO layer with structure similar to that of rock salt. The prototype compound Hg2Ba2YCU2O8-delta, is an insulator. Superconductivity is induced in the system by partially replacing yttrium with calcium.