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The thermal stability of the superconducting magnet is one of the important issues for MRI system. In this work, the quench behavior of superconducting MgB2 magnet for MRI is studied by use of the finite element method (FEM) and finite difference method (FDM). This work considers a close winding coil subjected to a thermal disturbance that is a three-dimensional problem. The effective value is adopted in the physical properties of the magnet. The quench propagation velocity (QPV) in various conditions is computed by the parallel-tapes model beforehand. The quench characteristics of the MgB2 magnet with different parameters of superconducting wires are investigated. The effect of the initial quench location on the quench characteristics and the feasibility of dump resistor protection method for the MgB2 magnet are also discussed. The results show that the outer edge of magnet is the worst initial quench location, optimized MgB2/Fe/Cu MgB2 magnet has higher operating security, and the dump resistor protection method is feasible for the small and medium-sized MgB2 magnet.