Most research so far on trajectory tracking of free-floating space manipulators has assumed that the kinematics of the space manipulator is exactly known. However, when a space manipulator picks up different tools of unknown lengths or unknown gripping points, its kinematics and dynamics change and are difficult to derive exactly. Thus, in this paper, we have proposed a passivity based adaptive Jacobian controller for free-floating space manipulators. The proposed controller consists of a transposed Jacobian feedback and a dynamic compensation term. and the parameter adaptation laws are derived by Lyapunov-like stability analysis tools. It is shown that the end-effector motion tracking errors converge asymptotically. To avoid using spacecraft acceleration, we define a new reference velocity, which is called spacecraft reference velocity. in addition, we have also conducted passivity interpretation of the proposed controller to obtain some physical insight into its properties. Simulation results are presented to show the performance of the proposed controller. (C) 2009 Elsevier Ltd. All rights reserved.