This paper investigates the robustness of deep learning MR reconstruction models for adversarial attacks like new lesions, different anatomy and noise pollutions. Specifically, three popular MR reconstruction algorithms were selected to investigate this issue. Experimental results show that model-based deep learning MR reconstruction method is relatively more robust than end-to-end data-driven reconstruction networks when transfer to other organs or face new lesions. Data-driven approaches can achieve better results when the testing images follow similar distributions as the training images. Severe noise can be a big issue for both deep learning methods and the traditional method.