The concept of the beam propagation factor M2 is extended for chromatic laser beams. The definition of the beam propagation factor can be generalized with the weighted effective wavelength. Using the new definition of factor M2, the propagation of chromatic beams can be analyzed by the beam propagation factor M2 as same as that of monochromatic beams. A simple method to measure the chromatic beam factor M2 is demonstrated. The chromatic factor M2 is found invariable while the laser beam propagates through the dispersion-free ABCD system.