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Test-time adaptation (TTA) has increasingly been an important topic to efficiently tackle the cross-domain distribution shift at test time for medical images from different institutions. Previous TTA methods have a common limitation of using a fixed learning rate for all the test samples. Such a practice would be sub-optimal for TTA, because test data may arrive sequentially therefore the scale of distribution shift would change frequently. To address this problem, we propose a novel dynamic learning rate adjustment method for test-time adaptation, called DLTTA, which dynamically modulates the amount of weights update for each test image to account for the differences in their distribution shift. Specifically, our DLTTA is equipped with a memory bank based estimation scheme to effectively measure the discrepancy of a given test sample. Based on this estimated discrepancy, a dynamic learning rate adjustment strategy is then developed to achieve a suitable degree of adaptation for each test sample. The effectiveness and general applicability of our DLTTA is extensively demonstrated on three tasks including retinal optical coherence tomography (OCT) segmentation, histopathological image classification, and prostate 3D MRI segmentation. Our method achieves effective and fast test-time adaptation with consistent performance improvement over current state-of-the-art test-time adaptation methods. Code is available at: https://github.com/med-air/DLTTA.