This paper deals with a control method for a manipulator mounted on a free-floating space robot. A control method using the transpose of the Generalized Jacobian Matrix has been proposed. In contrast to many control methods using the inverse or pseudo-inverse matrix, the method guarantees the stability of the control system in the face of a singularity. This method, however, is developed on the assumption that all the parameters of the robot are known. That is, it is not sure whether the system stability can be ensured in the presence of parameter uncertainties. In this paper, we develop the adaptive control version. It is shown that the adaptive control system developed for the unknown parameters has the same stability property that the control system developed for the known parameters has.