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Click-through rate(CTR) prediction is a core task in cost-per-click(CPC) advertising systems and has been studied extensively by machine learning practitioners. While many existing methods have been successfully deployed in practice, most of them are built upon i.i.d.(independent and identically distributed) assumption, ignoring that the click data used for training and inference is collected through time and is intrinsically non-stationary and drifting. This mismatch will inevitably lead to sub-optimal performance. To address this problem, we formulate CTR prediction as a continual learning task and propose COLF, a hybrid COntinual Learning Framework for CTR prediction, which has a memory-based modular architecture that is designed to adapt, learn and give predictions continuously when faced with non-stationary drifting click data streams. Married with a memory population method that explicitly controls the discrepancy between memory and target data, COLF is able to gain positive knowledge from its historical experience and makes improved CTR predictions. Empirical evaluations on click log collected from a major shopping app in China demonstrate our method's superiority over existing methods. Additionally, we have deployed our method online and observed significant CTR and revenue improvement, which further demonstrates our method's efficacy.