The [GADV]-protein, consisting only of glycine (G), alanine (A), aspartic acid (D), and valine (V), is frequently studied as a candidate for a primitive protein that existed at the beginning of life on Earth. The number of proteogenic amino acids increased during evolution, and glutamic acid may have been added as the fifth amino acid. In this study, we used molecular dynamics simulations to estimate the conformation of random peptides when glutamate is added to G, A, D, and V ([GADVE]), when leucine is added ([GADVL]), and when the frequency of alanine is doubled ([GADVA]). The results showed that the secondary structure contents of the [GADVE]-peptide and [GADVL]-peptide were higher than that of the [GADVA]-peptide. Although the [GADVL]-peptide had a higher secondary structure formation ability than the [GADVE]-peptide, it was less water soluble, suggesting that it may not be a primitive protein. The [GA(D/E)V]-peptide with G:A:D:V:E = 2:2:1:2:1 according to the occurrence ratio in the codon table also increased the secondary structure contents compared to the [GADV]-peptide, indicating that the addition of glutamic acid increased the structure formation ability of the primitive protein candidates.