The complex polarization propagator method [J. Chem. Phys. 123, 194103 (2005)] has been employed in conjunction with density functional theory and gauge-including atomic orbitals in order to determine the near-edge x-ray absorption and natural circular dichroism spectra of L-alanine in its neutral and zwitterionic forms. Results are presented for the K-edges of carbon, nitrogen, and oxygen. In contrast to traditional methods, the proposed approach enables a direct determination of the spectra at an arbitrary frequency instead of focusing on the rotatory strengths for individual electronic transitions. The propagator includes a complete set of nonredundant electron-transfer operators and allows for full core-hole relaxation. The theoretical spectrum at the nitrogen K-edge of the zwitterion compares well with the experimental spectrum.