A previously unreported family of electrically insulating rare-earth borates, RbBaR(BO3)(2) (R = Y, Gd-Yb), was designed and then successfully obtained by traditional solid-state reaction. They crystallize in a monoclinic crystal system space group P2(1)/m (No. 11). They feature triangular planar rare-earth (R) lattices, which are part of, for example, [Yb(BO3)(2)](3-) infinite 2D layers. These R-based triangular lattices are stacked with layers of crystallographically ordered Rb and Ba atoms to build the 3D structures. Polycrystalline samples of RbBaR(BO3)(2) were used to study the elementary magnetic properties, and millimeter-size RbBaYb(BO3)(2) single crystals were grown by spontaneous nucleation for further anisotropic magnetic characterization. Antiferromagnetic spin interactions are observed for all magnetic compounds, and no long-range magnetic ordering is found down to 1.8 K. Our results suggest that this RbBaR(BO3)(2) (R = Gd-Yb) family may be of further interest both experimentally and theoretically as highly geometrically frustrated magnets.