A dispersion measurement apparatus includes: a pulse generator to output optical pulses including an optical pulse with a first wavelength and an optical pulse with a second wavelength to an optical transmission path, the second wavelength being different from the first wavelength; a reception pulse analyzer including an optical receiver that receives the optical pulses output by the pulse generator, and an analyzer that performs a wavelet transform on an electrical pulse output through the reception performed by the optical receiver; and a calculator to detect, based on a result of the wavelet transform, a time difference between the optical pulse with the first wavelength and the optical pulse with the second wavelength, and to determine dispersion in the optical transmission path.