We propose an improvement of the interferometric method used up to now to measure the chromatic dispersion in single mode optical fibers, which enables dispersion measurements in higher-order modes over a wide spectral range. To selectively excite a specific mode, a spatial light modulator was used in the reflective configuration to generate an appropriate phase distribution across an input supercontinuum beam. We demonstrate the feasibility of the proposed approach using chromatic dispersion measurements of the six lowest order spatial modes supported by an optical fiber in the spectral range from 450 to 1600 nm. Moreover, we present the results of numerical simulations that confirm sufficient selectivity of higher-order mode excitation.