The term ''Grid'' was coined to describe a form of distributed computing in which hardware and software resources from disparate sites are virtualized to provide applications with a single, powerful computing infrastructure. In fact, the term comes from an analogy with the electrical power grid infrastructure, since researchers expect applications to access Grid resources as transparently as electricity is now consumed. However, ''plugging'' applications into the Grid is still very difficult because current toolkits force programmers to take into account many complex details when coding applications for the Grid. This paper presents JGRIM, a middleware for easy ''gridification'' of ordinary Java applications. The main goal of JGRIM is to make the task of porting applications to the Grid easier and, at the same time, provide facilities to easily address efficiency issues when gridifying an application. An experimental evaluation showing the feasibility of our approach and some of its benefits is also reported.