We propose a novel optical dispersion measurement system using dual-heterodyne mixing to measure the relative phase. The system can realize parallel measurement of the relative phases between adjacent frequencies by introducing optical modulators to generate optical sidebands from a laser light source and an arrayed waveguide grating to separate the sidebands. To realize a wide dispersion range, different frequency intervals for the adjacent frequencies were combined in the system. One is the three-frequency optical dispersion measurement system (three-frequency measurement), which has been developed to measure the relative phase between adjacent peaks of an optical frequency spectrum with intervals of 25 GHz generated without any frequency scanning. The other is the four-frequency optical dispersion measurement system (four-frequency measurement) with intervals of 2 GHz generated from the three-frequency sets to expand the measurement range. The experimental results using single-mode optical fibers of different lengths from 0 to 90 km indicated the dispersion slope to be $16.8\mathrm{ps}/\mathrm{nm}/\mathrm{km}$ with a measurement range of $2500\mathrm{ps}/\mathrm{nm}$ and an uncertainty of less than $1\mathrm{ps}/\mathrm{nm}$. The proposed system provides advantages to enable parallel measurement on a frequency axis without a high-speed (GHz) photodetector, even though GHz spacing on the optical scale is used, thus reflecting the dual-heterodyne mixing.