A new series of stable noble gas-Lewis acid compounds NgBeH(3)BeR, NgBeH(3)BR(+), and NgBH(3)BR(2+) (R = F, H, CH3, Ng = He-Rn) with three 3c-2e H-bridged bonds have been predicted by use of the PBE0 and MP2 methods. The Ng7-Be/B bonds are strong and have large binding energies 35-130, 9-38, and 4-13 kcal/mol for the doubly charged cations, singly charged cations, and neutral molecules, respectively. The binding energy and strength of the Ng-Be/B bonds increase largely from He to Rn but are insensitive to electronegativity of the substituent R. The Ng-B bonds in NgBH(3)BR(2+) should be typical covalent bonds and the Ng-Be bonds in NgBeH(3)BR(+) for heavy Ng atoms Kr, Xe, and Rn have some covalent character. The three bridging-H atoms have characteristic infrared vibrational modes with large IR intensity to be detected in spectroscopy experiments.