This paper presents a Grid environment developed for analysis of MRI brain data on global Grids. In the current experiment, the MRI data analysis tasks are composed and formulated as a parameter sweep application. This application was deployed using the Gridbus Resource broker. The clusters in our Grid environment were managed using PBS and SGE. To execute tasks on remote resources, the Gridbus broker used SSH services for some resources and Globus middleware services for others for initiating execution and management. In this experiment, 16 x 8.1MB images and 28 x 16.3MB images were processed using a volumetric analysis method. The total waiting time was 1800s and the total processing time was 1279.30s. The broker overhead was 521s. Completing this analysis on a single machine could take over twenty hours. This Grid architecture provides a useful time-saving analysis tool for neuroimaging applications.