We propose a new algorithm for blind source separation (BSS), in which independent component analysis (ICA) and beamforming are combined to resolve the low-convergence problem through optimization in ICA. The proposed method consists of the following three parts: (1) frequency-domain ICA with direction-of-arrival (DOA) estimation, (2) null beamforming based on the estimated DOA, and (3) integration of (1) and (2) based on the algorithm diversity in both iteration and frequency domain. The inverse of the mixing matrix obtained by ICA is temporally substituted by the matrix based on null beamforming through iterative optimization, and the temporal alternation between ICA and beamforming can realize fast- and high-convergence optimization. The results of the signal separation experiments reveal that the signal separation performance of the proposed algorithm is superior to that of the conventional ICA-based BSS method, even under reverberant conditions.