Bursty topic discovery aims to automatically identify bursty events and continuously keep track of known events. The existing methods focus on the topic model. However, the sparsity of short text brings the challenge to the traditional topic models because the words are too few to learn from the original corpus. To tackle this problem, we propose a Sparse Topic Model (STM) for bursty topic discovery. First, we distinguish the modeling between the bursty topic and the common topic to detect the change of the words in time and discover the bursty words. Second, we introduce “Spike and Slab” prior to decouple the sparsity and smoothness of a distribution. The bursty words are leveraged to achieve automatic discovery of the bursty topics. Finally, to evaluate the effectiveness of our proposed algorithm, we collect Sina weibo dataset to conduct various experiments. Both qualitative and quantitative evaluations demonstrate that the proposed STM algorithm outperforms favorably against several state-of-the-art methods