Security in traditional computer networks requires authentication, access control, integrity, privacy and non-repudiation, which can be also be applied to assure security in grid computing. Related works to authentication, authorization, and privacy in grids have been presented in the literature. However, there is a need to guarantee to grid users and administrators that grid machines are not corrupting or modifying data distributed in the shared resources. Thus, the main goal of this paper is to propose an approach to verify distributed data integrity in grid machines. This approach applies an algorithm to test resources in a grid, which provides more security and makes also possible the integrity verification of external entities.