Coarse mesh rebalance (CMR) method is formulated for the acceleration of fission source iteration (FSI) in the multigroup transport theory analysis of subcritical source-driven systems. The within-group equations are solved by diamond-differenced S-N method and CMR has been employed also for the acceleration of scattering source iterations. By numerical experiments, carried out in spherical geometry, stability and performance characteristics of the proposed acceleration are determined and assessed. Systems containing a central nonmultiplying source region and an outer multiplying blanket region are considered. CMR is stable provided that the number of coarse mesh regions in the blanket is in a stability interval between a minimum and a maximum value, irrespective of the fine mesh used in S-N calculations. Maximum acceleration is obtained for an optimum number of blanket coarse mesh regions which is also independent of the fine mesh. Both the width of the stability interval and the optimum speed-up ratio (execution time ratio of the unaccelerated run to the accelerated one) increases as the system becomes optically thicker. If we let the system approach criticality by increasing the blanket size, the number of FSIs increases dramatically if no acceleration is employed. For such slightly subcritical systems, very high speed-up ratios are obtained with CMR acceleration whose performance is independent of the criticality level.