We study the phase stability of a double-minimum potential system in order to obtain a method of stabilizing a solid phase by interaction. The present double-minimum potential is the Lennard–Jones–Gauss (LJG) potential, which has a Gaussian pocket as well as a standard Lennard–Jones minimum. In the LJG potential system, the coexistence density and freezing pressure are calculated by the thermodynamic perturbation method. The calculation shows that the stability of a solid phase is significantly affected by the position of the second minimum (Gaussian pocket). In particular, there are positions ensuring the high stability of fcc and bcc crystals. We explain the reason for the high stability by comparing the position of the second minimum (Gaussian pocket) with the crystal structure.