—A matrix converter is a voltage/current source AC/AC frequency converter. In grid-connected operation of a variable-speed permanent magnet synchronous wind power generator, the matrix converter is normally controlled as a voltage source converter. In this control method, the generator-side voltage is synthesized from the grid-side voltage source. However, in the stand-alone mode of operation, the grid-side stiff voltage source is not available, and the input filter of the matrix converter is unstable. In this article, a new control method is presented that controls a permanent magnet synchronous wind generator in a stand-alone mode with a matrix converter as a current source converter. The proposed method is so fast that it can control the matrix converter small capacitor voltage despite the generator large inductance and without any input filter instability. A multi-pole permanent magnet synchronous wind generator is simulated to prove the performance of the proposed control strategy.