This Letter proposes a novel technique for automatic position offset calibration for permanent-magnet synchronous machine (PMSM) drives. Contrary to existing methods, the proposed technique estimates and compensates for the position offset without using machine true parameters or signal injection, which is possible under the condition of zero-current control at high enough speed where parameter-dependent terms are eliminated. To achieve this condition using uncertain parameters, speed control with absolute value feedback and model-free current control are devised. Additionally, under this condition, not only the misalignment of the position sensor but also the sensor delay can be considered as the position offset, which improves the accuracy of the calibration. The proposed approach will be verified by experimental results.