With the increasing popularity of online chatting, stickers are becoming important in our online communication. Selecting appropriate stickers in open-domain dialogue requires a comprehensive understanding of both dialogues and stickers, as well as the relationship between the two types of modalities. To tackle these challenges, we propose a multitask learning method comprised of three auxiliary tasks to enhance the understanding of dialogue history, emotion and semantic meaning of stickers. Extensive experiments conducted on a recent challenging dataset show that our model can better combine the multimodal information and achieve significantly higher accuracy over strong baselines. Ablation study further verifies the effectiveness of each auxiliary task. Our code is available at https://github.com/nonstopfor/Sticker-Selection.