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The element-by-element finite element method (EBE-FEM) parallel algorithm has been realized on Compute Unified Device Architecture (CUDA) platform in this paper. An improved fast color marking method (FCM) combined with tabu search algorithm is proposed to solve the problem that the elements sharing a node wait for accessing the same memory space in parallel computation. The elements in the same color can be processed at the same time without waiting. This method can get more even color grouping faster than the classical coloring method (CCM).  Combining it with the EBE parallel algorithm can achieve faster element-level operations. The validity and accuracy of the method has been verified by comparing the computed results with the analytical solution of the magnetic field produced by the solenoid. The parallel program is applied to analyze the main magnetic field of a single-phase transformer, which shows higher speedup performance.