Blue-phase liquid crystals form three-dimensional structures in a self-organizing manner and are similar to living tissue structures such as the teeth of mice and collagen tissues. This study presents numerical results regarding the conditions under which blue-phase liquid crystals occur. The Monte Carlo simulations are performed by employing an improved Lennard–Jones potential that considers anisotropy and chirality. The conditions for the formation of the blue phase, which vary with respect to the chirality, are examined first. The relationship between the anisotropic parameters and the chiral parameter for the formation of the blue phase is discussed. Identical blue-phase structures are obtained, even when the cell size and molecular number are varied drastically. This discussion is useful for considering the scale-up problem, which is almost always a difficult issue for molecular-scale simulations.