We propose a novel memory-enhancing mechanism for recurrent neural networks that exploits the effect of human cognitive appraisal in sequential assessment tasks. We conceptualize the memory-enhancing mechanism as Reinforcement Memory Unit (RMU) that contains an appraisal state together with two positive and negative reinforcement memories. The two reinforcement memories are decayed or strengthened by stronger stimulus. Thereafter the appraisal state is updated through the competition of positive and negative reinforcement memories. Therefore, RMU can learn the appraisal variation under violent changing of the stimuli for estimating human affective experience. As shown in the experiments of video quality assessment and video quality of experience tasks, the proposed reinforcement memory unit achieves superior performance among recurrent neural networks, that demonstrates the effectiveness of RMU for modeling human cognitive appraisal.