Bilibili’s scientific popularization sub-sectors under the knowledge category provides an excellent learning platform for a broad audience. However, some science popularization videos on the platform suffer from low popularity. Research on how to identify scientifically influential videos remains underexplored. Against this backdrop, this research defines a video influence calculation method based on entropy weight, tailored to Bilibili’s specific characteristics, and constructs a Multimodal CNN-Transformer model (MMCT) that integrates text, social, audio, image, and content modalities to predict the influence of scientific popularization videos on Bilibili. Experiments are conducted on video influence regression prediction using crawled Bilibili video data, and the model’s effectiveness is validated through ablation studies. Furthermore, benchmarks are set to verify the effectiveness of the multimodal feature fusion in video influence classification. The results indicate that MMCT achieves an SRCC of 0.7895, improving by 0.0566 compared to the baseline model, while MSE decreases by 0.4022 compared to the baseline model. This study contributes to Bilibili’s ability to identify highly influential popular science videos, thereby enhancing the platform’s commercial value and competitiveness while promoting the effective and high-quality dissemination of popular science knowledge on Bilibili.