We present a novel spectrum-slicing method for measuring the chromatic dispersion of an optical fiber in Fourier-domain low-coherence interferometry. Broadband spectral interference data obtained from a low-coherence interferometer is sliced with Gaussian window functions. Each sliced spectral datum is used to calculate a relative group delay with Fourier transformation at the peak wavelength of a narrow window function. We have demonstrated that our proposed method is very powerful and simple for measuring chromatic dispersion and second-order dispersion in optical fibers and optical devices. Comparison of the proposed method with a conventional measurement method agrees within 0.5%.