A computationally efficient method is proposed for estimating the directions-of-arrival (DOAs) of signals impinging on a uniform linear array (ULA), based on partial a priori knowledge of signal sources. Unlike the classical MUSIC algorithm, the proposed method merely needs the forward recursion of the multistage Wiener filter (MSWF) to find the noise subspace and does not involve an estimate of the array covariance matrix as well as its eigendecomposition. Thereby, the proposed method is computationally efficient. Numerical results are given to illustrate the performance of the proposed method.