We propose a new algorithm for the blind source separation (BSS) approach in which independent component analysis (ICA) and frequency subband beamforming interpolation are combined. The slow convergence of the optimization of the separation filters is a problem in ICA. Our approach to resolving this problem is based on the relationship between ICA and null beamforming (NBF). The proposed method consists of the following three parts: (I) a frequency subband selector part for learning ICA, (II) a frequency domain ICA part with direction-of-arrivals (DOA) estimation of sound sources, and (III) an interpolation part in which null beamforming constructed with the estimated DOA is used. The results of the signal separation experiments under a reverberant condition reveal that the convergence speed is superior to that of the conventional ICA-based BSS methods.