The Method of Moments(MoM) combined with Multi-Layer Fast Multipole Algorithm (MLFMA) and Adaptive Cross Approximation(ACA) is proposed to calculate the electromagnetic characteristics of the target. The computation of the scattering of electrically large composite targets is speeded up and the memory requirement is reduced. For the near-field region of self-acting target, MoM and MLFMA are combined to speed up the matrix vector multiplication, reduce the storage and decrease the complexity of calculation. The far-field impedance matrix has a low rank characteristic and can be compressed by ACA to speed-up the filling rate of the matrix. Matrix filling is stored sequentially according to the interaction among the blocks divided by tree structure. ACA algorithm is utilized to solve the problem of the compression of matrix between each block and block. The proposed hybrid algorithm based on ACA can compress the impedance matrix of the coupling between two targets, reduce the filling time and the required memory of the matrix. At the same time, the computation time of matrix vectors can be shortened in the iterative process, thus the total time of electromagnetic scattering calculation can be reduced greatly. Numerical simulation results show that the algorithm is more efficient than the traditional method, and the accuracy of electromagnetic scattering is consistent.