The high-pressure synthesis of new hydrides of Mg-RE-H systems, where RE = La, Ce and Pr, were conducted by using a cubic-anvil-type apparatus, and their crystal structure, thermal stabilities and hydrogen contents were investigated. In MgH2-xmol%REH (REH = LaH3, CeH2.5 and PrH3) new hydrides with primitive tetragonal structure were synthesized around x = 25 - 33 under GPa-order high pressures. The lattice constants were a = 0.8193 nm, c = 0.5028 nm, a = 0.8118 nm, c = 0.4979 nm and a = 0.8058 nm, c= 0.4970 nm at x = 25 in Mg-La, Ce and Pr systems, respectively. The hydrogen contents of the novel compounds were 4.1 mass%, 3.7 mass% and 3.9 mass% in Mg-La, Ce and Pr systems, respectively, and the chemical formulas were found to correspond to Mg3LaH9, Mg3CeH8.1 and Mg3PrH9. The new hydrides decomposed into Mg and rare-earth hydride at about 600 K (Mg3LaH9: 614 K, Mg3CeH8.1: 609 K, Mg3PrH9: 630 K) with an endothermic reaction.