Previous Sentiment Analysis (SA) studies have demonstrated that exploring sentiment cues from multiple synchronized modalities can effectively improve the SA results. Unfortunately, until now there is no publicly available dataset for multimodal SA of the stock market. Existing datasets for stock market SA only provide textual stock comments, which usually contain words with ambiguous sentiments or even sarcasm words expressing opposite sentiments of literal meaning. To address this issue, we introduce a Fine-grained Multimodal Sentiment Analysis dataset built upon 1,247 Stock Comment videos, called FMSA-SC. It provides both multimodal sentiment annotations for the videos and unimodal sentiment annotations for the textual, visual, and acoustic modalities of the videos. In addition, FMSA-SC also provides fine-grained annotations that align text at the phrase level with visual and acoustic modalities. Furthermore, we present a new fine-grained multimodal multi-task framework as the baseline for multimodal SA on the FMSA-SC. Data and codes are available at https://github.com/sunlitsong/FMSA-SC-dataset.git .