At present, Mashup development has attracted much attention in the field of software engineering. It is the focus of this article to use existing open APIs to meet the needs of Mashup developers. Therefore, how to select the most appropriate open API for a specific user requirement is a crucial problem to be solved. We propose a Hybrid Open API Selection Approach for Mashup development (HyOASAM), which consists of two basic approaches: one is a user-story-driven open API discovery approach, and the other is multidimensional-information-matrix- (MIM-) based open API recommendation approach. The open API discovery approach introduces user stories in agile development to capture Mashup requirements. First, it extracts three components from user stories, and then, it extracts three corresponding properties from open API descriptions. Next, the similarity calculation is performed on two sets of data. The open API recommendation approach first uses MIM to store open APIs, Mashups, and the invoking relationship between them. Second, it enters the matrix obtained in the previous step into a factorization machine model to calculate the association scores between the Mashups and the open APIs, and TOP-N open API lists for creating the Mashup are obtained. Finally, experimental comparison and analysis are carried out on the PWeb dataset. The experimental results show that our approach has improved significantly.