By using the Nambu-Jona-Lasinio model with a tensor-type four-point interaction between quarks, it is shown that there exists a possibility of a spin polarized phase in quark matter at finite temperature and density.
When there exists the spin polarization, the spontaneous magnetization may occur if the effect of the anomalous magnetic moment of quark is taken into account.
An implication to the compact star objects with strong magnetic field is discussed when the spin polarization occurs.