To improve the performance of mobile web service, a new transport protocol, QUIC, has been recently proposed. However, for large-scale real-world deployments, deciding whether and when to use QUIC in mobile web service is challenging. Complex temporal correlation of network conditions, high spatial heterogeneity of users in a nationwide deployment, and limited resources on mobile devices all affect the selection of transport protocols. In this paper, we present WiseTrans to adaptively switch transport protocols for mobile web service online and improve the completion time of web requests. WiseTrans introduces machine learning techniques to deal with temporal heterogeneity, makes decisions with historical information to handle spatial heterogeneity, and switches transport protocols at the request level to reach both high performance and acceptable overhead. We implement WiseTrans on two platforms (Android and iOS) in a popular mobile web service application of Company B. Comprehensive experiments demonstrate that WiseTrans can reduce request completion time by up to 26.5% on average compared to the usage of a single protocol.