We propose a novel acoustic beamforming method using blind source separation (BSS) techniques based on non-negative matrix factorization (NMF). In conventional mask-based ap- proaches, hard or soft masks are estimated and beamforming is performed using speech and noise spatial covariance matri- ces calculated from masked noisy observations, but the phase information of the target speech is not adequately preserved. In the proposed method, we perform complex-domain source sep- aration based on multi-channel NMF with rank-1 spatial model (rank-1 MNMF) to obtain a speech spatial covariance matrix for estimating a steering vector for the target speech utilizing the separated speech observation in each time-frequency bin. This accurate steering vector estimation is effectively combined with our novel noise mask prediction method using multi-channel robust NMF (MRNMF) to construct a Maximum Likelihood (ML) beamformer that achieved a better speech recognition per- formance than a state-of-the-art DNN-based beamformer with no environment-specific training. Superiority of the phase pre- serving source separation to real-valued masks in beamforming is also confirmed through ASR experiments.