The quantum effects on the propagation circularly polarized waves have been investigated in electron magnetized quantum plasmas. We obtain the dispersion equations of the propagation of circularly polarized laser beam through cold plasma. The results show that the laser can be propagated due to the quantum effects which enhance the propagation phase velocity. For this purpose, the quantum hydrodynamic (QHD) equations with magnetic field and Maxwell’s equations system is used to derive these dispersion relations. The perturbed electron density and current due to the in- teraction of laser beam with quantum plasma have been investigated. It is shown that the external magnetic field which is parallel to the propagation waves has strong effect on the dispersion relation for the laser propagation in quantum model than the classical regime