Traditional beamformer based on the interference-plus-noise covariance matrix (INCM) reconstruction achieves high performance in the case of high input signal-to-noise ratio (SNR), however the performance of which is barely improved in the low input SNR with high complexity. Focused on the problem above, a novel method in view of the effectiveness of reconstruction is proposed in this paper, which can reduce computational complexity with little performance degradation under the low input SNR. The central idea is that the determination factor (DF), which is defined by whether the desired signal can be estimated, is introduced as the criterion of the INCM reconstruction. Firstly, the Multiple Signal Classification (MUSIC) is used to exploit the relationship between the DF and the input SNR. Then whether the INCM is necessary to reconstruct is determined by the DF. Finally, the corresponding INCM is calculated. Theoretical analysis and simulations show that the proposed beamformer obtains better performance compared with the reconstruction-based beamformer and can balance the complexity and performance well.