Multimedia event detection has been receiving increasing attention in recent years. Besides recognizing an event, the discovery of evidences (which is refered to as "recounting") is also crucial for user to better understand the searching result. Due to the difficulty of evidence annotation, only limited supervision of event labels are available for training a recounting model. To deal with the problem, we propose a weakly supervised evidence discovery method based on self-paced learning framework, which follows a learning process from easy "evidences" to gradually more complex ones, and simultaneously exploit more and more positive evidence samples from numerous weakly annotated video segments. Moreover, to evaluate our method quantitatively, we also propose two metrics, \textit{PctOverlap} and \textit{F1-score}, for measuring the performance of evidence localization specifically. The experiments are conducted on a subset of TRECVID MED dataset and demonstrate the promising results obtained by our method.