The phase A of the comb-like poly(alpha-n-octadecyl-beta,L-aspartate) has been investigated using atomistically detailed computer simulations. Four independent polymer chains of 13 residues were constructed and packed in an orthogonal simulation box with periodic continuation conditions. A set of microstructures was obtained by Configurational Bias Monte Carlo generation. Some torsional angles of the alkyl side chains were constrained in order to facilitate the crystallization of paraffinic chains. The resulting microstructures have provided a detailed description of the structural behaviour of this phase allowing to characterize some related properties. The most relevant results have been compared with those recently obtained for the phase B and with the available experimental data.