Influence maximization (IM) aims to find a subset of k nodes that can maximize the final active node set under an information diffusion model. With the development and popularity of social networks, the IM problem plays an essential role in various applications, such as public opinion analysis, viral marketing, and rumor early warning. However, most of the existing IM solutions have not accessed the risk of negative information from nodes in the future. In reality, a company may face economic loss when negative information breaks out of its spokesman. Therefore, a crisis assessment oriented and topic-based IM problem (TIM-CA) is proposed, which is utilized to model the IM problem by considering the crisis assessment (CA) and topics of users. To solve this problem, we propose a maximum influence arborescence model-based algorithm for TIM-CA, namely, MIA-TIM-CA. The proposed algorithm consists of crisis degree calculation, topic relevance calculation, and influence spread evaluation. More importantly, as for crisis degree calculation, it considers self-, topology-, and topic-based crisis degrees for each node. At the influence spread evaluation stage, MIA-TIM-CA proposes two functions to evaluate the node's importance and node influence spread. Extensive experiments on two real-world social networks demonstrate that our MIA-TIM-CA outperforms all comparison algorithms on influence spread, crisis score, and running time.