The method of quasi‐reversibility (QR) (Lattes and Lions, 1969) has been used previously to solve the diffusion equation with reversed time. We develop a quasi‐reversible solution to a convection‐dispersion equation by solving the QR diffusion operator in a moving coordinate system. The solution procedure is applied to the problem of recovering the history of a groundwater contaminant plume from observations of its present conditions. This approach to the plume history problem is potentially superior to the Tikhonov regularization approach used by Skaggs and Kabala (1994) because it is easier to implement and readily allows for space‐ and time‐dependent transport parameters. However, our results for a few example problems suggest that the QR procedure is less accurate than the regularization technique. Thus the easy implementation and improved generality of the QR procedure come at the expense of accuracy; this trade‐off will have to be weighed if the QR technique is to be used. Copyright 1995 by the American Geophysical Union.