Natural amino acid-based ionic liquids (AAILs) composed of deprotonated amino acids, [AA]-, as anions and hydroxylated imidazolium cations provide an eco-friendly nontoxic IL family with the growing number of chemical and biochemical revolutionary applications. In this paper, the transport properties of four AAILs composed of 1-(2-hydroxyethyl)-3-methylimidazolium ([HOemim]+) and 1-ethyl-3-methylimidazolium ([emim]+) cations with alaninate and glycinate anions were studied by molecular dynamics (MD) simulations. A nonpolarizable all-atom force field with the scaled charge (±0.8e) on each of the ions was applied and compared with the unit charge model in some cases. The tunable effects of the presence of the hydroxyl group in the side chain of the imidazolium cation, the type of amino acid anion, and the varied temperature on the dynamical behavior of AAILs were investigated in detail. The experimentally compatible trends of the simulated ionic self-diffusion coefficients, ionic conductivity, and ionicity were found to be inverse to the viscosity and ionic association of these ILs as [emim][Gly] > [emim][Ala] > [HOemim][Gly] > [HOemim][Ala]. The main reason behind these trends is the higher ability of the hydroxylated cation for the hydrogen-bond formation with [AA]-. The mean square displacement (MSD), self-diffusion, and transference number of imidazolium cations are larger than those of [AA]- anions, except in the case of [HOemim][Gly]. It was found that the activation energy for diffusion of [AA]- is lower than that of [HOemim]+ but higher than that of [emim]+ in [HOemim][AA] and [emim][AA] ILs, respectively. The computed velocity autocorrelation function (VACF) showed that [Gly]-, as the lightest ion, has the shortest mean collision time and velocity randomization time among the ions, especially in the [HOemim][Gly] IL. Replacing [emim]+ with [HOemim]+, similar to the effect of decreasing temperature, causes significant decreasing of the ionic self-diffusion and increasing of the well depth of the first minimum of the ionic VACFs. Current findings show that introducing suitable functional groups in the side chain of imidazolium cations can be a viable approach for efficient engineering design and fine-tuning of the transport properties of these AAILs.