In general, humans tend to devalue a delayed reward. Such delay discounting is a theoretical and computational concept in which the discount factor influences the time scale of the trade-off between delay of reward and amount of reward. The discount factor relies on the individual’s ability to evaluate the future reward. Using functional magnetic resonance imaging, we investigated brain mechanisms for reward valuation at different individual discount factors in a delayed reward choice task. In the task, participants were required to select small/immediate or large/delayed rewards to maximize the total reward over time. The discount factor for each participant individually was calculated from the behavioral data based on an exponential discounting model. The estimated value of a future reward increases as the expected delivery approaches, so the time course of these estimated values was computed based on each individual’s discount factor; each was entered into the regression analysis as an explanatory (independent) variable. After the region of interest was narrowed anatomically to the caudate, a peak coordinate was detected in each individual. A correlation analysis revealed that the location of the peak along the dorsal–ventral axis in the right caudate was positively correlated with the discount factor. This implies that individuals who showed a larger discount factor had peak activations in a more dorsal part of the right caudate associated with future reward prediction. This evidence also suggests that a higher ability to delay reward prediction might be related to activation of the more dorsal caudate.