In response to the increasing use of interactive artificial intelligence, the demand for the capacity to handle complex questions has increased. Multi-hop question generation aims to generate complex questions that requires multi-step reasoning over several documents. Previous studies have predominantly utilized end-to-end models, wherein questions are decoded based on the representation of context documents. However, these approaches lack the ability to explain the reasoning process behind the generated multi-hop questions. Additionally, the question rewriting approach, which incrementally increases the question complexity, also has limitations due to the requirement of labeling data for intermediate-stage questions. In this paper, we introduce an end-to-end question rewriting model that increases question complexity through sequential rewriting. The proposed model has the advantage of training with only the final multi-hop questions, without intermediate questions. Experimental results demonstrate the effectiveness of our model in generating complex questions, particularly 3- and 4-hop questions, which are appropriately paired with input answers. We also prove that our model logically and incrementally increases the complexity of questions, and the generated multi-hop questions are also beneficial for training question answering models.