A series of samples with a nominal composition of R3CaBa3Cu7Oy (abbreviated as R3137), where R = Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er and Tm, was prepared by a similar process as for an 80-K superconductor, La3CaBa3Cu7Oy. Most of the R3137 (except for R = Ce, Tb) had a tetragonal triple-perovskite phase like La3137 identified from the XRD patterns, and they were superconducting except Pr3137. For R3+ radius larger than Dy3+ (0.908 Å), a single phase R3137 was observed, and their Tc(zero)' probably related to the rCu-o distance in the copper-oxygen layer, was spread from 85 to 76 K with a maximum for the Eu3137. Oxygen stoichiometry of these R3137 was slightly decreased with decreasing lanthanide radii. The hole concentration, (Cu-O), was found between 0.47 and 0.38/unit cell. For Smaller R3+ ions, residual resistivity was found in the superconducting samples due to the existence of second phase. From the structural study of La3137, it was known that part of the lanthanide ions had to be fitted into the bigger Ba-site. Because ionic radii of the heavy lanthanides (R3+ < Ho3+ = 0.894 Å) were too small to be located at the Ba-site, it was rather difficult to prepare these single phase R3137.