Security is an important concern in providing the infrastructure for the implementation of general purpose computational grids. However, most grid implementations focus their security concerns in correctly authenticating users and hosts and in the communications among them. In most cases, application security is left to the underlying operating system. This can be a problem when a “malicious” application is executed. In this work, we introduce the GridBox architecture, that aims to provide additional security for GRID applications, using Access Control Lists and sandbox functionality for GRID tasks.