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We calculate the spin-flavor precession (SFP) of Dirac neutrinos induced by strong magnetic fields and finite neutrino magnetic moments in dense matter. As found in the case of Majorana neutrinos, the SFP of Dirac neutrinos is enhanced by the large magnetic field potential and suppressed by large matter potentials composed of the baryon density and the electron fraction. The SFP is possible irrespective of the large baryon density when the electron fraction is close to 1/3. The diagonal neutrino magnetic moments that are prohibited for Majorana neutrinos enable the spin precession of Dirac neutrinos without any flavor mixing. With supernova hydrodynamics simulation data, we discuss the possibility of the SFP of both Dirac and Majorana neutrinos in core-collapse supernovae. The SFP of Dirac neutrinos occurs at a radius where the electron fraction is 1/3. The required magnetic field of the proto-neutron star for the SFP is a few 10^{14} G at any explosion time. For the Majorana neutrinos, the required magnetic field fluctuates from 10^{13} G to 10^{15} G. Such a fluctuation of the magnetic field is more sensitive to the numerical scheme of the neutrino transport in the supernova simulation.