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This paper presents the design of an XYZ nano-manipulator as well as the model based high precision tracking control of the nano-manipulating system. Aiming at large range and high mechanical bandwidth, the proposed mechanical design employs compound bridge-type amplifiers to increase the workspace without significant drop of stiffness. To further improve the system tracking performance and avoid possible actuator saturations, a robust anti-windup tracking control architecture combining a parallel internal-model based controller and an anti-windup compensator is adopted for the trajectory tracking of the designed nano-manipulating system. As a theoretical extension on a recent result [17], we further investigate the robust stability condition of the closed-loop system and formulate the optimization design of the anti-windup compensators as a two block H∞ optimization problem solvable with the Nehari approach. Real time control experiments demonstrate excellent tracking performance and saturation compensation capability with tracking precision error less than 0.28%, which significantly outperforms relevant algorithms in the literature. We would like to thank the financial support from the NSFC under Grant Nos. 61327003 and 51775319 , the National Key Research and Development Program of China under Grant No. 2017YFF0105903 , and the Fundamental Research Funds of Shandong University under Grant No. 2015JC034 .