Physiological needs evoke motivational drives that produce natural behaviors for survival. In previous studies, the temporally intertwined dynamics of need and motivation have made it challenging to differentiate these two components. On the basis of classic homeostatic theories, we established a normative framework to derive computational models for need-encoding and motivation-encoding neurons. By combining the model-based predictions and naturalistic experimental paradigms, we demonstrated that agouti-related peptide (AgRP) and lateral hypothalamic leptin receptor (LHLepR) neuronal activities encode need and motivation, respectively. Our model further explains the difference in the dynamics of appetitive behaviors induced by optogenetic stimulation of AgRP or LHLepR neurons. Our study provides a normative modeling framework that explains how hypothalamic neurons separately encode need and motivation in the mammalian brain.