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Question Generation (QG), as a challenging Natural Language Processing task, aims at generating questions based on given answers and context. Existing QG methods mainly focus on building or training models for specific QG datasets. These works are subject to two major limitations: (1) They are dedicated to specific QG formats (e.g., answer-extraction or multi-choice QG), therefore, if we want to address a new format of QG, a re-design of the QG model is required. (2) Optimal performance is only achieved on the dataset they were just trained on. As a result, we have to train and keep various QG models for different QG datasets, which is resource-intensive and ungeneralizable. To solve the problems, we propose a model named Unified-QG based on lifelong learning techniques, which can continually learn QG tasks across different datasets and formats. Specifically, we first build a format-convert encoding to transform different kinds of QG formats into a unified representation. Then, a method named \emph{STRIDER} (\emph{S}imilari\emph{T}y \emph{R}egular\emph{I}zed \emph{D}ifficult \emph{E}xample \emph{R}eplay) is built to alleviate catastrophic forgetting in continual QG learning. Extensive experiments were conducted on $8$ QG datasets across $4$ QG formats (answer-extraction, answer-abstraction, multi-choice, and boolean QG) to demonstrate the effectiveness of our approach. Experimental results demonstrate that our Unified-QG can effectively and continually adapt to QG tasks when datasets and formats vary. In addition, we verify the ability of a single trained Unified-QG model in improving $8$ Question Answering (QA) systems' performance through generating synthetic QA data.