This paper deals with a digital adaptive control for a manipulator mounted on a space robot after it captures an unknown object. Most control methods are based on the supposition that all physical parameters of the space robot are known. However, if the end-effector catches an unknown object, the physical parameters of the robot are changed, and the control performance gets worse. In this paper, we propose two types of digital adaptive control algorithm using a discretized kinematic equation. Computer simulation was used to make it clear that the control performance can be improved by using either of the proposed methods.