A control system for a work vehicle includes a controller. The controller receives actual topography information of a work target. The controller determines a design surface that is positioned below the actual topography. The controller generates a command signal to move a work implement of the work vehicle along the design surface. The controller determines if slip of the work vehicle has occurred. Upon determining that slip has occurred, the controller changes the design surface to a position equal to or higher than a blade tip position of the work implement when the slip occurred.