In our continued exploratory synthesis of compounds containing transition-metal oxide magnetic nanostructures, a new copper(II) phosphate phase, Cs2Cu3P4O14 (1), was isolated employing the mixed CsCl/2Csl molten flux. The X-ray single-crystal structural analysis shows that the Cs2Cu3P4O14 phase crystallizes in a monoclinic space group with a = 7.920(2) angstrom, b = 10.795(2) angstrom, c = 7.796(2) angstrom, beta = 103.90(3)degrees, and V = 646.9(2) angstrom(3); P2(1)/c (No. 14); Z = 2. The structure has been refined by the full-matrix least-squares method to a final solution with R1 = 0.0248, wR2 = 0.0553, and GOF = 1.02. The three-dimensional Cu-O-P framework exhibits pseudo-one-dimensional channels where the Cs+ cations reside. The framework consists of trimeric CuO4 square-planar units stacked in a staggered configuration. These CuO4 trimers are interlinked by the P2O7 units via vertex-sharing O atoms. The stacked CuO4 units are slanted with respect to the (CuCuCu)-Cu-...-Cu-... vector, resulting in additional Cu-O long bonds, 2.71 (1) angstrom, and a possibly shortened (CuCu)-Cu-... distance, 3.38(3) angstrom. I shows limited cation substitution with smaller alkali-metal cations; in fact, only a relatively small concentration of Cs+ can be substituted by Rb+ to form Cs(2-x)Rb(x)Cu(3)P4O(14) (0.0 <= x <= 0.8). The temperature-dependent magnetic susceptibility studies of 1 and its Rb-substituted analogues alpha = 0, 0.33, 0.50, and 0.80) reveal a weak ferromagnetic transition at T-c = similar to 14 K, which evidently is independent of the variation of x. In this paper, we report the synthesis, structure, and properties of the title compounds, as well as its brief comparison with the previously discovered Li2Cu3Si4O12 phase, which exhibits fused square-planar CuO4 trimers.