A grid service is a Web service that provides a set of well-defined interfaces a nd follows specific conventions. A grid service exception may occur in a process of behaviors related to requesting, responding, or running a grid service. Grid service exceptions deal with the run-time status and contextual information of grid services. A handler of exceptions mainly holds the configuration of a group of checkpoints, trace and rollback of services. The common approach to handling an exception is using a function to check out an error and sending the error co de to the caller, which may need a multi-level and consecutive behaviors, till t he error is sent to the function that responds it. If the linkage of these funct ions is weak, the whole process would fail. In a grid computing environment, an exception handler should not only reduce the internal propagation of error codes , but also make a transferable function to send the exception to an external uni t or a grid service. In terms of the grid architecture, the exception handler of a grid service is discussed and then an A/B-Back algorithm is proposed, which i s used to handle exceptions in a grid service. Finally, the test result based on the simulated experiment in Globus Toolkit 3.0 is given.