Wind energy conversion systems have become a key technology to harvest wind energy worldwide. In permanent magnet synchronous generator-based wind turbine systems, the rotor position is needed for variable speed control and it uses an encoder or a speed sensor. However, these sensors lead to some obstacles, such as additional weight and cost, increased noise, complexity and reliability issues. For these reasons, the development of new sensorless control methods has become critically important for wind turbine generators. This paper aims to develop a new sensorless and adaptive control method for a surface-mounted permanent magnet synchronous generator. The proposed method includes a new model reference adaptive system, which is used to estimate the rotor position and speed as an observer. Adaptive control is implemented in the pulse-width modulated current source converter. In the conventional model reference adaptive system, the proportional-integral controller is used in the adaptation mechanism. Moreover, the proportional-integral controller is generally tuned by the trial and error method, which is tedious and inaccurate. In contrast, the proposed method is based on model predictive control which eliminates the use of speed and position sensors and also improves the performance of model reference adaptive control systems. In this paper, the proposed predictive controller is modelled in MATLAB/SIMULINK and validated experimentally on a 6-kW wind turbine generator. Test results prove the effectiveness of the control strategy in terms of energy efficiency and dynamical adaptation to the wind turbine operational conditions. The experimental results also show that the control method has good dynamic response to parameter variations and external disturbances. Therefore, the developed technique will help increase the uptake of permanent magnet synchronous generators and model predictive control methods in the wind power industry.