Using the numerical solution of the time-dependent Schr(o)dinger equation of a one-dimensional model atom in a two-colour laser field, we have investigated the effects of the potential models on coherent control of atomic multiphoton ionization. It is found that the photoelectron spectra are obviously different for the long-range (Coulomb-like) and short-range (with no excited bound states) potential model atoms, which are produced by two-colour coherent control of atomic multiphoton ionization in a few laser cycles. Our results indicate that two-colour coherent control of atomic multiphoton ionization can be observed in simulations, depending on the choice of the model potentials.