Abstract: The higher order moment method is widely applied in the computational electromagnetics. In order to compute the electrically massive problems, this paper introduces a parallel adaptive cross approximation algorithm(ACA) to accelerate the higher order moment method. At first, the non-uniform rational B-Splines modeling (NURBS) is applied to divide the patches into groups. Then the ACA algorithm is used to compress the impedance matrix in the far zone, which is low in rank. Finally, the conjugate gradient method(CG) combined with the sparse pattern approximate inverse preconditioning(SPAI) is used to solve the matrix equation. Both the ACA compressing and the CG method are suitable for parallel computation. Numerical experiments show that the memory of the compressed matrix is much less than that of the original matrix, and the preconditioned CG method converges very fast. Besides, the massively parallel method often has a high efficiency.