This paper proposes an iterative learning control scheme for a redundant manipulator to acquire a skilled hand writing motion of its end-point specified on an arbitrary smooth surface. Firstly, the existence of a unique solution to the Lagrange equation of motion of the robot, whose end-point motion is coincident with a given desired end-point trajectory described in Cartesian coordinate system, is shown theoretically. Second, the iterative learning control signal that enables the robot end-point to trace a desired trajectory specified on an arbitrary smooth surface with fulfilling a desired contact force is designed. Next, a numerical simulation for the iterative learning scheme is conducted to show the effectiveness of the proposed controller, and its result is compared to a theoretically derived desired joint angle trajectory. This comparison shows that there exists a unique solution of the desired joint angle trajectory when an initial pose of the manipulator and a desired end-point trajectory on the constraint surface are given, even under the existence of holonomic constraint and joint redundancy.