Modeling the transport of groundwater contamination leads generally to problems wherein the continuity equation is coupled with the contaminant transport equation and Darcy's law. Such a system of equations is called the flow-transport system and is difficult to solve numerically. An optimal control, H1, least squares formulation, associated with a conjugate gradient algorithm, is proposed for solving the coupled flow and transport problem. At each time step, each discretized differential equation is transformed into an optimal control problem. This problem is then stated as an equivalent minimization problem. The objective function associated with the transport problem is chosen in such a way that it accurately represents the advective behavior of the equation for high values of the Peclet number. The Nazareth version of the conjugate gradient method is used for solving the problem iteratively. At each iteration, only the right-hand side of the equation is changed. Thus, the approach is attractive when large-scale problems must be solved. Analysis of the preconditioning of the coefficient matrix provides insight into the behavior of this approach. Validation runs for a one-dimensional example show accurate results for a wide range of Peclet and Courant numbers. ¿ American Geophysical Union 1993