Users' purchase behaviors are complex and dynamic, which are usually driven by various personal demands evolving with time. According to psychology and economic theories, user demands can be satisfied with a sequence of purchase behaviors, resulting in a basket of items. However, most of the existing works simply predict the next basket from a shallow perspective of (purchase) sequence data modeling without deep insight into the underlying factors which drive user purchase behaviors. In fact, filling a basket with multiple items is a process to incrementally satisfy a user's demand. Therefore, the key challenges to predict a user's next basket lie in (1) how to track the changes of the user's demand, and (2) how to satisfy her demand at a given moment. To this end, we propose an Evolving DEmand SAtisfaction (EvoDESA) model to model a user's demand evolution for next-basket prediction. In EvoDESA, a demand evolution module learns the dynamics of user demand over a sequence of basket-purchase behaviors. Then, a next-basket planning module effectively packs an optimal combination of items to best satisfy the user's current demand. Extensive experiments on three real-world transaction datasets demonstrate the considerable superiority of EvoDESA over the state-of-the-art approaches.