Multimode fibers (MMF) are remarkable high-capacity information channels. However, the MMF transmission is highly sensitive to external perturbations and environmental changes. Here, we show the successful binary image transmission using deep learning through a single MMF subject to dynamic shape variations. As a proof-of-concept experiment, we find that a convolutional neural network has excellent generalization capability with various MMF transmission states to accurately predict unknown information at the other end of the MMF at any of these states. Our results demonstrate that deep learning is a promising solution to address the high variability and randomness challenge of MMF based information channels. This deep-learning approach is the starting point of developing future high-capacity MMF optical systems and devices and is applicable to optical systems concerning other diffusing media.