This letter presents a new algorithm for blind dereverberation and echo cancellation based on independent component analysis (ICA) for actual acoustic signals. We focus on frequency domain ICA (FD-ICA) because its computational cost and speed of learning convergence are sufficiently reasonable for practical applications such as hands-free speech recognition. In applying conventional FD-ICA as a preprocessing of automatic speech recognition in noisy environments, one of the most critical problems is how to cope with reverberations. To extract a clean signal from the reverberant observation, we model the separation process in the short-time Fourier transform domain and apply the multiple input/output inverse-filtering theorem (MINT) to the FD-ICA separation model. A naive implementation of this method is computationally expensive, because its time complexity is the second order of reverberation time. Therefore, the main issue in dereverberation is to reduce the high computational cost of ICA. In this letter, we reduce the computational complexity to the linear order of the reverberation time by using two techniques: (1) a separation model based on the independence of delayed observed signals with MINT and (2) spatial sphering for preprocessing. Experiments show that the computational cost grows in proportion to the linear order of the reverberation time and that our method improves the word correctness of automatic speech recognition by 10 to 20 points in a RT 20 = 670 ms reverberant environment.