Speech separation algorithms are often used to separate the target speech from other interfering sources. However, purely neural network based speech separation systems often cause nonlinear distortion that is harmful for automatic speech recognition (ASR) systems. The conventional mask-based minimum variance distortionless response (MVDR) beamformer can be used to minimize the distortion, but comes with high level of residual noise. Furthermore, the matrix operations (e.g., matrix inversion) involved in the conventional MVDR solution are sometimes numerically unstable when jointly trained with neural networks. In this paper, we propose a novel all deep learning MVDR framework, where the matrix inversion and eigenvalue decomposition are replaced by two recurrent neural networks (RNNs), to resolve both issues at the same time. The proposed method can greatly reduce the residual noise while keeping the target speech undistorted by leveraging on the RNN-predicted frame-wise beamforming weights. The system is evaluated on a Mandarin audio-visual corpus and compared against several state-of-the-art (SOTA) speech separation systems. Experimental results demonstrate the superiority of the proposed method across several objective metrics and ASR accuracy.