Grid architecture is a fast evolving distributed computing architecture. The working of databases in the Grid architecture is not well understood. In view of changing distributed architecture we strongly feel that concurrency control issues should be revisited and reassessed for this new and evolving architecture. Implementing global lock table and global log records may not be practically possible in the Grid architecture due to the scalability issues. In this paper, we propose a correctness criterion and the Grid concurrency control protocol, which has the capability to deal with heterogeneity, autonomy, distribution and high volume of data in Grids. We then prove the correctness of the protocol followed by performance evaluation of the protocol.