We propose a new algorithm for blind source separation (BSS), in which frequency-domain independent component analysis (FDICA) and time-domain ICA (TDICA) are combined to achieve a superior source-separation performance under reverberant conditions. Generally speaking, conventional TDICA fails to separate source signals under heavily reverberant conditions because of the low convergence in the iterative learning of the inverse of the mixing system. On the other hand, the separation performance of conventional FDICA also degrades significantly because the independence assumption of narrow-band signals collapses when the number of subbands increases. In the proposed method, the separated signals of FDICA are regarded as the input signals for TDICA, and we can remove the residual crosstalk components of FDICA by using TDICA. The experimental results obtained under the reverberant condition reveal that the separation performance of the proposed method is superior to those of TDICA- and FDICA-based BSS methods.