Recent years see an increasing concern over the trustworthiness of Internet-based software. By analyzing the trustworthiness of Internet-based software and the nature of the Internet applications, we point out that, on the one hand, due to the openness and dynamic nature of the Internet, the identity trustworthiness and the capability trustworthiness of the software are facing serious challenges; on the other hand, in order to ensure the trustworthiness of the whole system, emerging computing paradigms based on the collaboration of autonomous software need some impacts on the behavior of the software. Here we put forward a conceptual model for the trustworthiness of Internet-based software, and propose a trustworthy assurance framework for Internet-based virtual computing environment (iVCE). This framework deals with the trustworthy properties of software on identity, capability and behavior in a combinated way. The authorization management in inter-domain computing environment, assurance on high availability of service and incentive mechanism for autonomic collaboration are taken as three core mechanisms of iVCE trustworthy assurance.