The paper proposes a novel inductive angular displacement sensor based on time-grating to measure large-diameter hollow rotating mechanical components in large science facilities. The sensor design includes a stator, a rotor with two layers of windings. The stator is fabricated according to the dimension of the rotor, which is the large-diameter hollow rotary mechanical components. Based on the electromagnetic induction, the theoretical model of angular displacement measurement is derived by mathematical equations in detail. The sensor design ensures integration of the large-diameter hollow rotating mechanical components with the stator, and solves the problem that the sensors cannot be coaxially installed in the closed-loop control process of large mechanical rotating parts. The performance of the sensor is evaluated by tests of the prototype sensor fabricated by printed circuit board technology, which manifests the effectiveness of the proposed sensor. The results demonstrate the peak-to-peak value of original dynamic error is 124 ″ over 0 ° - 360 ° range, and the measurement error mainly includes first-order and second-order harmonic components. Therefore, the original errors are reduced by optimizing the angular displacement algorithm of the sensor, optimized results demonstrate the final accuracy of the sensor is ±3.5 ″ over the 0 °- 360 ° measurement range.