A new series of copper oxyselenides RCuSeO (R=La, Sm, Gd and Y) have been prepared and studied by X-ray powder diffraction. The Sm-containing phase was determined to have a tetragonal crystal structure with the lattice parameters a=3.9512(1)angstrom and c=8.7157(2)angstrom, the space group of which is P4/nmm. Its structure is built of a fluorite type layer [Sm2O2] and an anti-fluorite type layer [Cu2Se2] stacking alternatively along c direction. The similarity of the diffraction patterns for the samples with R=La, Gd and Y to that of SmCuSeO suggests their assuming the same crystal structure.