Abstract: To address the problem that the measurement accuracy of the circular time-grating sensor is adversely affected by the large first harmonic wave error due to the non-concentricity of the stator and rotor during the installation process, this paper proposes a self-diagnostic measurement method of the absolute circular time-grating eccentric state based on the multi-reading heads structure. In this structure, a single reading-head and four independent reading-heads are respectively arranged in the inner and outer rings of the circular time-grating rotor. According to the phase comparison relationship between the inner and outer ring induction signals, the degree of sensor eccentricity is assessed to realize the self-diagnostic measurement function of the sensor under the eccentric state. The measuring system built by LabVIEW simultaneously processes the phase meter values of the single induction signal in the inner ring and the four induction signals in the outer ring, obtains the absolute position information of the sensor and displays the absolute angular displacement value. Our experimental results show the measurement error accuracy of the sensor prototype is ±1″ in the whole week after the adjustment and installation, substantially improving the measurement accuracy of the sensor.