This paper presents a reduced-order-extended-state-observer (RESO) based repetitive control (RC) method for a class of servo systems with mismatched state-dependent uncertainties and external disturbances. It aims to achieve high-accuracy tracking for periodic reference input by on-line estimating and compensating the effects of the state-dependent uncertatinties and disturbances. Firstly, using the measurable output and control input of the plant, an RESO is constructed to estimate the unmeasurable states and the total disturbance including uncertainties and external disturbances. Based on the estimates, a composite RC law is devised that dynamically compensates for the influence on the output of the total disturbance and ensure the precise tracking for the periodic reference signal. Then, based on the small gain theorem, both the stability criterion and design procedure of the closed-loop system are provided. Finally, simulational and experimental results demonstrate the effectiveness and superiority of the proposed method.