Asking questions is an important ability for a chatbot. Although there are existing works on question generation with a piece of descriptive text, it remains to be a very challenging problem. In this paper, we consider a new question generation problem which also requires the input of a target aspect in addition to a piece of descriptive text. The key reason for this new problem is that it has been found from practical applications that useful questions need to be targeted toward some relevant aspects. One almost never asks a random question in a conversation. Due to the fact that given a descriptive text, it is often possible to ask many types of questions, generating a question without knowing what it is about is of limited use. in order to solve this problem, we propose a novel neural network which is able to generate aspect-based questions. One major advantage of this model is that it can be trained directly using a question-answering corpus without requiring any additional annotations like annotating aspects in the questions or answers. Experimental results show that our proposed model outperforms the state-of-the-art question generation methods.