The Grid vision is to allow compute resources to be shared and utilised globally, with these distributed resources belonging to the same Virtual Organisation (VO). These resources execute jobs submitted by users, who are not in the resources' local domain and hence have no control over these resources. Conversely these users are not controlled by the resource owners. Certificates provide a common, useful security mechanism to overcome these barriers and set out access rights, but they do not guarantee that the resources, or users, can be trusted. This is due to the fact that resources and users may be unreliable; this situation may not be reflected in the users' perception of the reliability of the resource owner as a whole or vice versa. This paper describes a trust framework model for Grid computing, which enables users to execute their jobs on reliable and efficient resources, thereby satisfying clients' quality-of-service (QoS) requirements.