The dynamic nature of the Grid environment brings challenges to the services provisioning technique. A major aspect of Grid is to match demands for services with resources. Since resources and demands are fluctuating, Grid services provisioning need to be adjusted accordingly in responding to changes. In this paper, we propose a novel approach, Grid services migration, to enabling services provisioning on demand. The major motivation is to achieve the desired Quality of Service (QoS) such as performance, reliability, and etc. of Grid services on resources assembled dynamically responding to dynamic demand. In this paper, the technical characteristics of Grid services migration and its taxonomy are introduced. The Grid service migration algorithms are also presented. The Grid services migration framework with MAPE (Monitor, Analyze, Plan, and Execute) loop is proposed based on Open Grid Services Architecture (OGSA) and the prototype named Services Ecosystem, a resilient infrastructure for services provisioning on demand in Grid is developed. Demonstrations and experiments are conducted and results are presented to illustrate the capabilities of Grid services migration.