We report the first hyperpolarizability of a series of tryptophan-rich short peptides with the respective sequence KWK, KWWK, KWWWK, KWWKWWK, where W and K stand for tryptophan and lysine. The measurements were performed with the technique of hyper-Rayleigh scattering in the bulk of an aqueous Tris buffer solution at a pH of 8.5 and a salt concentration of 150 mM at the non-resonant fundamental wavelength of 784 nm. The first hyperpolarizability of the different peptides follows a simple additive model scaling with the number of tryptophan residues contained in the peptide. However, it appears that the first hyperpolarizability response of a single tryptophan residue in the peptide strongly differs from that of an isolated tryptophan. Hence, it is therefore demonstrated that the local environment of the tryptophan residues within the peptide strongly influences its nonlinear optical response. A comparison with the first hyperpolarizability of the natural peptide gramicidin A measured in trifluoroethanol (TFE) further confirms the key role of the local environment on the first hyperpolarizability of tryptophan residues in peptides.