Aluminum (Al) films with thickness of 100 nm were grown on unheated glass, silicon and mica substrates by electron beam evaporation. The deposition rates were adjusted in the range between 0.1 nm/s and 2 nm/s, the pressure in the vacuum chamber during deposition was lower than 1.10(-3) Pa. The structure and surface morphology of the as-deposited Al films were studied using scanning electron microscopy (SEM) and atomic force microscopy (AFM). SEM imaging of the films showed that the mean grain size of thin Al films on all of the substrates increased from 20 nm - 30 nm to 50 nm - 70 nm with increase of the deposition rate. Quantitative AFM characterization showed that for all substrates the root mean square surface roughness increases monotonically with increasing the deposition rate from 0.1 nm/s to 2 nm/s. The observed effects of the deposition rate on the grain size and surface roughness are explained by the fundamental characteristics of the island growth mode, the influence of the background gases and the surface morphology of the bare substrates.