Abstarct: Quarks are known as elementary particles in standard model. In normal situation they are confined inside hadrons. Many efforts have been taken to study free quarks in different condition of density and temperature. There is possibility of existence of the deconfinement quark in neutron stars. Under extreme condition of temperature and pressure, the familiar structure of matter breaks down; meanwhile the phase transition is expected. After the transition the stable form of matter is quark matter. Recent discovery of magnetars, which have huge magnetic field and came into a new class of compact stars, stimulate interest in the studying of their properties. In this thesis, the properties of spin polarized quark matter have been studied using a three dimensional model for polarized quark matter with a density dependent quark-quark (confining) potential. Calculation of our results show that the ground state energy of quark matter increases by increasing spin polarization and spontaneous phase transition to ferromagnetic state does not occur. We have also found that the equation of state becomes stiffer by increasing polarization.