The linear IR and two-dimensional (2D) IR spectra of the amide-I modes of the 12-residue beta-hairpin peptide tryptophan zipper-2 (SWTWENGKWTWK) and its two C-13 isotopomers were simulated, with local mode frequencies evaluated by two solution-phase peptide amide-I frequency maps proposed recently: an electrostatic potential map and an electrostatic field map. Both maps predict a set of nondegenerate local amide-I mode transition energies for the hairpin. Spectral simulations using both maps predict the main spectral features of the linear IR and 2D IR experimental results of the C-13-labeled and -unlabeled hairpin. The radial distribution functions obtained using trajectories from classical molecular dynamics simulations demonstrate different water distributions at different sites of the hairpin. Our results suggest that the observed difference of the C-13-shifted band, including its peak position and frequency distributions for different isotopomers, in both linear IR and 2D IR spectra, is likely to be due to the difference in the local environment of the solvated peptide. Ab initio density functional theory calculations show a residue-independent C-13 shift of the amide-I mode, further supporting the result. The variations of these shifts are attributed to the residue level heterogeneity of the electrostatic environment of the peptide. Our results show that 2D IR of peptide with single C-13 isotopic labeling can be used to probe the electrostatic environment of the peptide local structure.