Abstract: Since Slater suggested that a gap could be opened by magnetic ordering with spin-dependent electronic energy, applying magnetic field has been a powerful means to tune properties of Dirac fermion systems, especially of the 2D graphene system． Determinant quantum Monte Carlo (DQMC) method is used, to investigate phase transitions induced by Zeeman field in 2D graphene lattice． Competition between Coulomb repulsion U, disorder Δ and magnetic fields B drives semimetallic regime to insulating phases exhibiting different characters． Further, critical Zeeman field B_c triggering band-insulator is largely reduced by the presence of interaction and disorder． As magnetic field continues to increase, B-induced symmetry breaking introduces an antiferromagnetic (AFM) phase, and eventually the system enters a fully spin-polarized state． In correlated system, weak interaction would enhance the effect of magnetic field on AFM phase, while strong interaction larger than U_c=4.5 would inhibit this effect． Applying parallel magnetic fields provides the possibility to observe transport and magnetic transitions in real materials．