In order to predict the cost of construction projects more accurately for cross-sectional data such as housing costs, a fractional heterogeneous grey model based on the principle of similar information priority was proposed in this paper. The advantages of the proposed model are proved by the stability analysis of the solution. The similarity between predicted samples and existing samples was analyzed, and the priority order of cross-sectional information was distinguished according to the similarity of the index information. The factors affecting the cost of construction projects were sorted by similarity, and the samples with high similarity to predicted samples were ranked first. Since projects with similar influence factors tend to produce similar project costs, such a ranking method can effectively utilize the information of similar projects and help improve prediction accuracy. In addition, compared with the prediction results of other models, it is verified that the method of prioritizing similar information can obtain more accurate prediction results.