It is interesting to resolve coherent signals impinging upon a linear sensor array with low computational complexity in array signal processing. In this paper, a computationally efficient method of signal subspace fitting (SSF) for direction-of-arrival (DOA) estimation is developed, based on the multi-stage wiener filter (MSWF). To find the new signal subspace, the proposed method only needs to compute the matched filters in the forward recursion of the MSWF, does not involve the estimate of an array covariance matrix or any eigendecomposition, thus implying that the proposed method is computationally efficient. Numerical results show that the proposed method provides the comparable estimation accuracy with the classical weighted subspace fitting (WSF) method for uncorrelated signals at reasonably high SNR and reasonably large samples, and surpasses the latter for coherent signals in the case of low SNR and small samples. When SNR is low and the samples are small, the proposed method is less accurate than the classical WSF method for uncorrelated signals. This drawback is balanced by the computational advantage of the proposed method.