A new family of complex copper oxides, HgBa2RCu2O7 (R= La, Nd, Eu, Gd, Dy, Y), has been synthesized and studied by X-ray powder diffraction, transmission electron microscopy and EDS analysis. The crystal structure of one of these compounds was determined. The Hg-atoms are in rock salt like blocks alternating with perovskite like ones where the copper atoms are located. This family can be considered as a first example of Hg-containing complex copper oxides with intergrowth structures ("1212" structural type). Magnetic measurements down to 12 K did not show noticeable diamagnetic effects.