In order to realize sensorless control for brushless doubly-fed induction machine (BDFIM), this paper presents a model reference adaptive system (MRAS) observer, designed based on the error of the control winding current. Furthermore, a phase-locked loop (PLL) is employed to estimate the current winding position and rotor speed. Consequently, a detailed theoretical derivation proves that the MRAS observer is stable and the dynamic performance is good. Thus, it does not cause any estimated speed error in steady state. Moreover, the estimated position error is bounded and trivial, thus its effects on the sensorless control of the BDFIM are neglected. The correctness, feasibility, and robustness of the proposed sensorless control method are verified by means of experimental validation on a 30kW test rig.