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The acceleration of a nonlinear magnetic field analysis by parallelizing the finite element method (FEM) is examined using the graphics processing unit (GPU). It is shown that the speedup of the magnetic field analysis is realized by parallelizing the variable preconditioned conjugate gradient (VPCG) method. The Jacobi over-relaxation (JOR) method, conjugate residual (CR) method and conjugate gradient (CG) method are also applied in the variable preconditioning. The results of computations demonstrate that VPCG using the GPU significantly improve the performance. Especially, CG applied by variable preconditioned on GPU is 39 times faster than ICCG on a CPU.