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Future space programs will require an agile relative position and attitude control technology for spacecraft. Rendezvous and docking, capture of inoperative spacecraft and formation flight in orbit are the typical scenarios. One of the key technologies is designing the tracking controllers that can control the six degrees-of-freedom (d.o.f.) of spacecraft under the influence of physical parameter uncertainties and external disturbances. To achieve agility, the controller design must be formulated as nonlinear control problems where translational and rotational motions are dynamically coupled with each other. This paper proposes a tracking controller, proportional-integral-derivative (PID)-type H¨adaptive state feedback controller, that can attenuate disturbances. The proposed controller has positive definite gain matrices whose conditions to be satisfied are given by linear matrix inequalities. The properties of the proposed controller were evaluated through numerical studies and compared with those of existing controllers.