The research objective is a numerical study of cough droplets evaporation and dispersion in an indoor environment using the multi-component Eulerian-Lagrangian approach to understand the basic aerosol science of SARS-CoV-2-laden droplets spread through the quasi-quiescent air. These results revealed that the smaller droplet evaporates faster than the larger droplet over a considerable time difference due to the enlarged specific surface area for heat and mass transfer, whereas the higher relative humidity of the air plays an important role to increase evaporation time. It was found that the higher temperatures were affected to accelerate the mass transfer to be fast evaporating and the initial droplet diameter ≤ 120 μm was completely evaporated until became droplet nuclei because the droplets were floating and dispersing still within the domain. The evaporation time called the falling time of initial droplet diameter ≥ 140 μm was canceled in a short time due to the large droplets falling to trap the bottom wall boundary. Moreover, the lowest temperature has a longer evaporation time and the least falling time, and the shortest horizontal distance because the residual droplet mass is greater than others.