It is of great value to study consumer demand for safe foods in promoting the development of a safe food market system and the reduction of food safety risks, as well as foodborne diseases in China. This paper takes traceable pork as an example and constructs food safety information attributes with ex ante quality verification and ex post traceability. Interactions between safety information attributes and the consumer’s response to cost-driven price changes were investigated for 345 consumers in Wuxi City, Jiangsu Province, China, using a menu-based choice (MBC) experiment and multivariate probit (MVP) model as analysis tools. The results suggest that food safety information attributes are important to consumers, as the consumers preferred pork quality inspection attributes to pre-incident quality assurance functions. Therefore, it is beneficial to include pork quality inspection attributes in the traceable pork attribute systems during the initial construction of traceable pork markets in China. Attribute price was an important factor that affected consumers’ choice of information attributes. When customization cannot be achieved, a profile composed of elastic pork quality inspection attribute and supply chain–internal traceability attribute would be the most preferred traceable pork product in the market based on the need of building a fully functional traceable food system and reducing food safety risks. In addition, there was a strong substitution relationship between different information attributes, and there was heterogeneity in consumers’ choice of information attributes. Therefore, the government should support manufacturers in producing multi-level safe food to meet diverse consumer demand.