Grid computing states the computation which supports geographically distributed heterogeneous resources sharing occurring in large-scale global distributed computing. The participants, including resource providers and requesters, involved in the computation originally belong to different administrative domains. In order to integrate resources and perform global cooperations, global policies have to be agreed to form the virtual organizations. Because the effective participants of virtual organizations are distributed and large-scale, describing a globalized grid application or a grid security solution is such a complicated problem. This study is aimed to propose a new modelling language, including related utilities, for modelling grid systems. The new modelling language is called Script, which is designed for grid computing and security solutions used in grid computing. It provides several simple reductions and a clear model architecture to model global applications. In addition, the security solutions and other distributed computing architectures are also available by means of the language. A Script model can be verified by a model verifier to validate the correctness of application before real implementation. From the mathematical point of view, an operational semantics of Script is also proposed. This thesis demonstrates the capability of the modelling language for wide-area distributed and grid computing. It demonstrates the functionalities to model grid scenarios and grid security solutions. Furthermore, a virtual organization solution is also presented in this thesis. This solution mainly focuses on the use of resource sharing and delegation, based on a web-services based grid application. It also demonstrates the capabilities of "Single Sign-On" and identity federation.