Online depth learning is the problem of consistently adapting a depth estimation model to handle a continuously changing environment. This problem is challenging due to the network easily overfits on the current environment and forgets its past experiences. To address such problem , this paper presents a novel Learning to Prevent Forgetting (LPF) method for online mono-depth adaptation to new target domains in unsupervised manner. Instead of updating the universal parameters, LPF learns adapter modules to efficiently adjust the feature representation and distribution without losing the pre-learned knowledge in online condition. Specifically, to adapt temporal-continuous depth patterns in videos, we introduce a novel meta-learning approach to learn adapter modules by combining online adaptation process into the learning objective. To further avoid overfitting, we propose a novel temporal-consistent regu-larization to harmonize the gradient descent procedure at each online learning step. Extensive evaluations on real-world datasets demonstrate that the proposed method, with very limited parameters, significantly improves the estimation quality.