Inductive sensors commonly used in Active Magnetic Bearings (AMBs) comprise soft-magnetic cores on stators and sensor targets on rotors. The rotor position is estimated based on values of inductances of sensor coils wound around the cores. These sensors are often easier to use than eddy-current sensors, but their readings can be affected by stray magnetic fields from AMB actuators. For radial sensors this problem can be mitigated by using two diametrically-opposite sensor heads in differential connection, however the same cannot be done for axial sensors. In addition, the axial sensors often need to be located as close as possible to axial actuators, where the stray fields are higher, in order to minimize changes of the actuator operating gaps caused by differences in thermal expansions of the rotor and the stator. The axial sensor presented in this paper has been developed to address primarily the issue of sensitivity to external fields. The closest kin of the proposed sensor is the axial inductive edge sensor. Because the magnetic excitation flux in the new sensor is maintained nearly constant during the operation, it was given a name “a constant-flux edge sensor”. A prototype of the new sensor has been built and tested.