The traditional displacement measurement interferometer (DMI) provides elegant performance by straight interference fringe movement counting to convert a phase calculation into an image motion calculation. However, it cannot be applied to a curve surface displacement measurement. The counting of the movement of irregular fringes is not achievable. We provide an adaptive moiré technique with a vortex phase to realize micro displacement measurement of a freeform surface with any continuous shape. The technique produces straight moiré fringes that rotate in a circle regardless of the shape of interference fringes and tested surface shapes. The vortex phase is used to record only one interferogram before the measurement for subsequent data processing, and then it no longer participates in the displacement measurement process. Therefore, this technology can be employed to remold traditional DMIs. Simulations and experiments validating the method are presented.