The first critical micelle concentration (CMC) of the ionic surfactant sodium dodecyl sulfate (SDS) in diluted aqueous solution has been determined at room temperature from the investigation of the bulk viscosity, at several concentrations of SDS, by means of coarse-grain molecular dynamics simulations. The coarse-grained model molecules at the mesoscale level are adopted. The bulk viscosity of SDS was calculated at several millimolar concentrations of SDS in water using the MARTINI force field by means of NVT shear Mesocite molecular dynamics. The definition of each bead in the MARTINI force field is established, as well as their radius, volume, and mass. The effect of the size of the simulation box on the obtained CMC has been investigated, as well as the effect of the number of SDS molecules, in the simulations, on the formation of aggregates. The CMC, which was obtained from a graph of the calculated viscosities versus concentration, is in good agreement with the reported experimental data and does not depend on the size of the box used in the simulation. The formation of a spherical micelle-like aggregate is observed, where the dodecyl sulfate tails point inward and the heads point outward the aggregation micelle, in accordance with experimental observations. The advantage of using coarse-grain molecular dynamics is the possibility of treating explicitly charged beads, applying a shear flow for viscosity calculation, and processing much larger spatial and temporal scales than atomistic molecular dynamics can. Furthermore, the CMC of SDS obtained with the coarse grained model is in much better agreement with the experimental value than the value obtained with atomistic simulations.