The Gauss-Seidel line relaxation method is modified for the simulation of viscous flows on massively parallel computers. The resulting data-parallel line relaxation method is shown to have good convergence properties for a series of test cases. The new method requires significantly more memory than the previously developed data-parallel relaxation methods, but it reaches a steady-state solution in much less time for all cases tested to date. In addition, the data-parallel line relaxation method shows good convergence properties even on the high-cell-aspect-ratio grids required to simulate high-Reynolds-number flows. The new method is implemented using message passing on the Cray T3E, and the parallel performance of the method on this machine is discussed. The data-parallel line relaxation method combines the fast convergence of the Gauss-Seidel line relaxation method with a high parallel efficiency and thus shows promise for large-scale simulation of viscous flows.