Social interactions enhance human memories, but little is known about how the neural mechanisms underlying episodic memories are modulated by rewarding outcomes in social interactions. To investigate this, fMRI data were recorded while healthy young adults encoded unfamiliar faces in either a competition or a control task. In the competition task, participants encoded opponents' faces in the rock-paper-scissors game, where trial-by-trial outcomes of Win, Draw, and Lose for participants were shown by facial expressions of opponents (Angry, Neutral, and Happy). In the control task, participants encoded faces by assessing facial expressions. After encoding, participants recognized faces previously learned. Behavioral data showed that emotional valence for opponents' Angry faces as the Win outcome was rated positively in the competition task, whereas the rating for Angry faces was rated negatively in the control task, and that Angry faces were remembered more accurately than Neutral or Happy faces in both tasks. fMRI data showed that activation in the medial orbitofrontal cortex (mOFC) paralleled the pattern of valence ratings, with greater activation for the Win than Draw or Lose conditions of the competition task, and the Angry condition of the control task. Moreover, functional connectivity between the mOFC and hippocampus was increased in Win compared to Angry, and the mOFC-hippocampus functional connectivity predicted individual differences in subsequent memory performance only in Win of the competition task, but not in any other conditions of the two tasks. These results demonstrate that the memory enhancement by context-dependent social rewards involves interactions between reward- and memory-related regions.