AMB (Active Magnetic Bearing) technology based multi-degree-of-freedom positioning systems is a very promising solution to many precise motion problems. In some applications, such as the photolithography process, AMB based positioning system can be used to carry tools of unknown geometry and mass. To avoid the positioning stage tracking performance degradation due to unknown payload, adaptive control methods should be used. Although the subject of adaptive control algorithms for the AMB based rotating machinery was widely studied in the past, due to some differences, the available results can not be applied in a straight-forward manner to the precise AMB based positioning systems. This paper contributes to the field of precise AMB based positioning stages by presenting design and implementation of an adaptive control algorithm for a 1DOF (degree-of-freedom) AMB based suspension system. In this study we assume that the payload and electromagnetic coefficient values of the plant are unknown and only the output measurements are available as a feedback. In addition, the control currents computed by the presented algorithm are free of a bias term. The control law in this papers solves the trajectory tracking problem, and its effectiveness was verified experimentally.