How to improve the speed of MRI is a standing problem in the field of magnetic resonance. A commonly used approach for acceleration is multi-coil scan. However, when the acceleration factor exceeds 4, the image quality obtained by traditional compressed sensing magnetic resonance imaging (CS-MRI) reconstruction algorithms becomes unsatisfactory. In this study, we propose a multi-coil MRI image reconstruction method named as ISTAVS algorithm based on physical model. It combines the ISTA algorithm with the splitting idea of VS-Net, and is expanded into an ISTAVS-Net. Each iteration step is combined with the network module, which has higher interpretability than black box U-Net. The residual mechanism is introduced into the ISTAVS-Net to increase the non-linear expression ability and accuracy. Sparse transformation, shrinkage threshold and regularization parameter are automatically learned during training, which increases the flexibility of reconstruction. The test results of the Globus knee dataset show that the ISTAVS-Net outperforms traditional L1-ESPIRiT and ISTA algorithm by multiple indicators, including the improvement of image quality and performance metrics over U-Net, ISTA-Net+ and VS-Net at different acceleration factors, and the ability to recover tissue details at high acceleration factors. The proposed network demonstrates good robustness and is more suitable for fast and high-quality reconstruction of data acquired on clinical MR scanners, thereby can expand the application range of MRI.