How to provide continued and smooth access to web services from smartphones under unstable network or during network disconnections is an important issue to be solved. In the past decade, many methods for service caching are proposed, however, a significant concern is commonly overlooked in these methods: a variety of contexts, namely, how to maintain the availability of mobile services for smartphones under a variety of mobile network conditions, such as high-speed network, unstable network, and no network access. In this paper, we propose a context-aware RESTful service delivery (CARSD) approach to address the above issue. The CARSD approach is encapsulated as client-side libraries to be utilized by mobile applications to invoke backend RESTful services. CARSD can perform different actions for different network conditions, such as prefetching service responses and using cached service in high speed wireless network, only using cached service in unstable wireless network, and allowing the user to request cached service response from other users when no wireless network can be accessed. The implementation and experiments demonstrate that the proposed CARSD approach can effectively improve service availability and shorten service response time in various network conditions.