In this paper, we present the Predicting Media Memorability task, which is proposed as part of the MediaEval 2018 Benchmarking Initiative for Multimedia Evaluation. Participants are expected to design systems that automatically predict memorability scores for videos, which reflect the probability of a video being remembered. In contrast to previous work in image memorability prediction, where memorability was measured a few minutes after memorization, the proposed dataset comes with short-term and long-term memorability annotations. All task characteristics are described, namely: the task's challenges and breakthrough, the released data set and ground truth, the required participant runs and the evaluation metrics.