Compressed sensing (CS) is an efficient method to reconstruct MR image from small sampled data in $k$-space and accelerate the acquisition of MRI. In this work, we propose a novel deep geometric distillation network which combines the merits of model-based and deep learning-based CS-MRI methods, it can be theoretically guaranteed to improve geometric texture details of a linear reconstruction. Firstly, we unfold the model-based CS-MRI optimization problem into two sub-problems that consist of image linear approximation and image geometric compensation. Secondly, geometric compensation sub-problem for distilling lost texture details in approximation stage can be expanded by Taylor expansion to design a geometric distillation module fusing features of different geometric characteristic domains. Additionally, we use a learnable version with adaptive initialization of the step-length parameter, which allows model more flexibility that can lead to convergent smoothly. Numerical experiments verify its superiority over other state-of-the-art CS-MRI reconstruction approaches. The source code will be available at url{https://github.com/fanxiaohong/Deep-Geometric-Distillation-Network-for-CS-MRI}
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