G protein-coupled receptors (GPCRs), which are indispensable to life and also implicated in a number of diseases, construct important drug targets. For the efficient structure-guided drug design, however, their structural stabilities must be enhanced. An amino-acid mutation is known to possibly lead to the enhancement, but currently available experimental and theoretical methods for identifying stabilizing mutations suffer such drawbacks as the incapability of exploring the whole mutational space with minor effort and the unambiguous physical origin of the enhanced or lowered stability. In general, after the identification is successfully made for a GPCR, the whole procedure must be followed all over again for the identification for another GPCR. Here we report a theoretical strategy by which many different GPCRs can be considered at the same time. The strategy is illustrated for three GPCRs of Class A in the inactive state. We argue that a mutation of the residue at a position of NBW = 3.39 (NBW is the Ballesteros-Weinstein number), a hot-spot residue, leads to substantially higher stability for significantly many GPCRs of Class A in the inactive state. The most stabilizing mutations of the residues with NBW = 3.39 are then identified for two of the three GPCRs, using the improved version of our free-energy function. These identifications are experimentally corroborated, which is followed by the determination of new three-dimensional (3D) structures for the two GPCRs. We expect that on the basis of the strategy, the 3D structures of many GPCRs of Class A can be solved for the first time in succession.