A magnetohydrodynamic (MHD) accelerator is proposed as a next generation propulsion system. The fundamental acceleration performance has been, so far, evaluated using one-dimensional (1-D) numerical analysis. However, the actual phenomena in the accelerator channel are highly coupled with boundary layers and with electrode phenomena and are three-dimensional. In this paper, research for investigating the three-dimensional (3-D) phenomena of an MHD accelerator is described. The validity of the 3-D numerical analysis is assessed through comparisons with the results of 1-D analysis. An existence of a local Hall current not predicted through 1-D analysis enhances the Joule dissipation and induces a secondary flow. It was found that a significant local Hall current influences the growth of the velocity overshoot, and this phenomenon is promoted particularly in a high Hall parameter environment. This study of 3-D analysis offers a more realistic prediction of the accelerator performance of the MHD accelerator than that of the 1-D predictions. (C) 2007 Elsevier Ltd. All rights reserved.