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Underwater robots in shallow waters usually suffer from strong wave forces, which may frequently exceed robot's control constraints. Learning-based controllers are suitable for disturbance rejection control, but the excessive disturbances heavily affect the state transition in Markov Decision Process (MDP) or Partially Observable Markov Decision Process (POMDP). Also, pure learning procedures on targeted system may encounter damaging exploratory actions or unpredictable system variations, and training exclusively on a prior model usually cannot address model mismatch from the targeted system. In this paper, we propose a transfer learning framework that adapts a control policy for excessive disturbance rejection of an underwater robot under dynamics model mismatch. A modular network of learning policies is applied, composed of a Generalized Control Policy (GCP) and an Online Disturbance Identification Model (ODI). GCP is first trained over a wide array of disturbance waveforms. ODI then learns to use past states and actions of the system to predict the disturbance waveforms which are provided as input to GCP (along with the system state). A transfer reinforcement learning algorithm using Transition Mismatch Compensation (TMC) is developed based on the modular architecture, that learns an additional compensatory policy through minimizing mismatch of transitions predicted by the two dynamics models of the source and target tasks. We demonstrated on a pose regulation task in simulation that TMC is able to successfully reject the disturbances and stabilize the robot under an empirical model of the robot system, meanwhile improve sample efficiency.