With the rapid development of Internet and big data technology, various online social network platforms have been established, producing massive information every day. Hot topic discovery aims to dig out meaningful content that users commonly concern about from the massive information on the Internet. Most of the existing hot topic discovery methods focus on a single network data source, and can hardly grasp hot spots as a whole, nor meet the challenges of text sparsity and topic hotness evaluation in cross-network scenarios. This paper proposes a novel hot topic discovery method across social network based on an im-proved LDA model, which first integrates the text information from multiple social network platforms into a unified data set, then obtains the potential topic distribution in the text through the improved LDA model. Finally, it adopts a heat evaluation method based on the word frequency of topic label words to take the latent topic with the highest heat value as a hot topic. This paper obtains data from the online social networks and constructs a cross-network topic discovery data set. The experimental results demonstrate the superiority of the proposed method compared to baseline methods.