Service-oriented grids are grid computing systems built with the notion of service-oriented architecture (SOA). Using two major abstract concepts, services and connections between services, each grid application is designed as a collection of looselycoupled services in an implementation independent manner. In service-oriented grids, the non-functional aspects of services and connections (e.g., message transmission and security) should be described separately from their functional aspects because different applications use services and connections in different nonfunctional requirements. This paper presents a UML profile to graphically specify and maintain non-functional aspects in service-oriented grids as implementation independent UML models. The UML models are transformed into implementation specific code by a model-driven development tool. This paper demonstrates how the proposed UML profile is used in model-driven development of service-oriented grid applications.