This paper presents the first input-output robust control design for the trajectory following problem of a flexible-joint robot manipulator. The proposed design provides a class of controllers which only require position and velocity feedback and ensure global stability. The resulting stability is that the tracking error can be made to be smaller than a design parameter arbitrarily chosen by the designer. The proposed control is robust since it guarantees tracking performance in the presence of high-order nonlinear uncertainties including unknown joint elasticity, unknown parameters, load variation, and disturbances. Practically, it is more important that no measurement on acceleration, jerk, or position and velocity deformation is required.