Using Web APIs registered in service sharing communities for mobile APP development can not only reduce development period and cost, but also fully reuse state-of-the-art research outcomes in broad domain so as to ensure up-to-date APP development and applications. However, the big volume of available APIs in Web communities as well as their differences make it difficult for APIs selection considering compatibility, preferred partial APIs and expected APIs functions which are often of high variety. Accordingly, how to recommend a set of functional-satisfactory and compatibility-optimal APIs based on the APP developer's multiple function expectation and pre-chosen partial APIs is on demand as a significant challenge for successful APP development. To address this challenge, we first construct a Web APIs correlation graph that incorporates functional descriptions and compatibility information of Web APIs, and then propose a correlation graph-based approach for personalized and compatible Web APIs recommendation in mobile APP development. Finally, through extensive experiments on a real dataset crawled from Web APIs websites, we prove the feasibility of our proposed recommendation approach.