Computational Grids are emerging as a new infrastructure for Internet-based parallel and distributed computing. They enable the sharing, exchange, discovery, and aggregation of resources distributed across multiple administrative domains, organizations and enterprises. To accomplish this, Grids need infrastructure that supports various services: security, uniform access, resource management, scheduling, application composition, computational economy, and accounting. Although several initiatives are engaged in the development of Grid technologies, Grid accounting issues are yet to be addressed. To overcome this limitation, we propose a new infrastructure called Grid Bank that provides services for accounting. The support of computational economy and accounting services can lead to a self-regulated accountability in grid computing. This paper presents requirements of Grid accounting and different economic models within which it can operate and proposes a Grid Accounting Services Architecture to meet them. The paper highlights implementation issues with a detailed discussion on the format for various records/databases that the GridBank needs to maintain. It also presents protocols for interaction between the GridBank and various components within Grid computing environments.