We present spectroscopic diffraction phase microscopy (sDPM) as a method capable of measuring quantitative phase images at multiple wavelengths. sDPM uses a spatial light modulator at the Fourier plane of a lens to select desired wavelengths from the white light illumination of a grating. The quantitative phase information at different wavelengths allows us to decouple the refractive index and the thickness from the phase shift induced by biological cells. We demonstrate the capability of the setup by dispersion measurements of microsphere beads and RBCs.