Scaling laws of fast growth of collisionless double tearing modes in the linear phase are studied numerically by a reduced magnetohydrodynamics model in a cylindrical plasma. It is found that in the case ρs ≪ de, with de the electron inertial skin depth and ρs the ion sound gyroradius, the scaling of the linear growth rate changes gradually from to as the rational surface separation Δrs increases. In the case de ≪ ρs, on the other hand, the scaling shifts gradually from or to or as Δrs increases. In the small Δrs regime, furthermore, it is shown that for short wavelength unstable modes, the scaling on de and ρs as their poloidal mode number varies is similar to that as Δrs does. In addition, ρs is found to play an important role in reducing the scaling dependence on de. These numerical scaling laws are testified to be reasonable in comparison with previous analytical theories, based on the similarity of physical characteristics of the same Δ' categories in tearing modes, where Δ' is the linear instability parameter for tearing modes. Finally, the characteristics of the second unstable eigenmode with different mode numbers, under the influence of de and ρs, are obtained and analysed.