The social networks such as Facebook, Line or Wechat recommend the friends for the users based on user's personal data such as common contact list or mobility traces. However, outsourcing users' personal information to the cloud for friend matching will raise a serious privacy concern due to the potential risk of data abusing. In this study, we propose a novel Scalable and Privacy-preserving Friend Matching protocol, or SPFM in short, which aims to provide a scalable friend matching and recommendation solutions without revealing the user's personal data to the cloud. Different from the previous works which involves multiple rounds of protocols, SPFM presents a scalable solution which can prevent honest-but-curious mobile cloud from obtaining the original data and support the friend matching of multiple users simultaneously. We give detailed feasibility and security analysis on SPFM and its accuracy and security have been well demonstrated via extensive simulations. The result show that our scheme works even better when original data is large.