The minimum variance distortionless response (MVDR) beamformer is an effective method for improving the target speech in noisy environments. However, the traditional MVDR filter can be computationally inefficient and lacks robustness, particularly for arrays with a large number of sensors. This inefficiency arises from the need to compute the inverse of the noise covariance matrix. Low-rank beamforming, which exploits the low-rank characteristics of microphone observations in array processing, offers a potential solution to these challenges. This paper introduces a framework for low-rank MVDR beamforming, where the global beamformer is represented as a Kronecker product of several sub-filters, which are optimized iteratively using an MVDR-based criterion. Simulation results show that the proposed approach significantly enhances computational efficiency while improving speech enhancement performance.