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Irradiation damage to zirconium alloys (e.g., zirconium niobium (Zr-Nb) alloy) is the key to the design of fission-reactor structural materials and fuel rod cladding materials. Atomic scale computational simulations such as molecular dynamics and first principles are often needed to understand the physical mechanism of irradiation damage. For the simulation of randomly substitutional solid solution, it is necessary to construct large-sized supercells that can reflect the random distribution characteristics of alloy elements. However, it is not suitable to use large-size supercells (such as ≥ 200 atoms) for first principle calculation, due to the large computational cost. Special quasirandom supercells (SQS) are usually used for first principles calculation. The SQS can partly reflect the random distribution characteristics of alloy elements, but it only corresponds to one configuration for specific components, hence whether this model can reflect the statistical average of multiple local configurations in a real randomly substitutional solid solution is still an open question, and needs further studying and verifying. Molecular dynamics (MD) simulation can be carried out on the randomly substitutional solid solution with a larger scale based on random substitution (RSS) method, these supercells include more local configurations. Therefore, the MD studies of Zr-Nb alloy are carried out for the RSS and SQS-extended supercells. The critical size of RSS supercell which can truly reflect the statistical properties of solid solution alloy is determined. Then the lattice constant, formation energy and energy-volume relationship of SQS-extended supercell of Zr-Nb alloy and a series of RSS supercells are calculated and compared. The results show that the lattice constants, the formation energy and energy volume curves of the solid solution obtained by SQS supercell simulation are close to a series of corresponding statistical values of the physical properties of RSS supercells, so the SQS supercells can be used to study the random substitution of solid solution alloys.