In many real-world machine learning problems, feature values are not readily available. To make predictions, some of the missing features have to be acquired, which can incur a cost in money, computational time, or human time, depending on the problem domain. This leads us to the problem of choosing which features to use at the prediction time. The chosen features should increase the prediction accuracy for a low cost, but determining which features will do that is challenging. The choice should take into account the previously acquired feature values as well as the feature costs. This paper proposes a novel approach to address this problem. The proposed approach chooses the most useful features adaptively based on how relevant they are for the prediction task as well as what the corresponding feature costs are. Our approach uses a generic neural network architecture, which is suitable for a wide range of problems. We evaluate our approach on three cost-sensitive datasets, including Yahoo! Learning to Rank Competition dataset as well as two health datasets. We show that our approach achieves high accuracy with a lower cost than the current state-of-the-art approaches.