A new method is described for the measurement of material dispersion in optical fibers. It consists in using LED sources, which emit a relatively large spectrum of 100-200 nm width, and selecting the various wavelength by means of a monochromator; the differences in time delay between the various wavelengths are measured in a very accurate way by sinusoidally modulating the LED at a fixed frequency and measuring the phase difference. The wavelength range 0. 75-1. 35 nm has been covered with 4 LED's, and a precise determination of the wavelength of zero material dispersion has been obtained.