In this paper, a fault diagnosis method is proposed based on component-wise expectation maximization algorithm and k-means algorithm, and it is applied to diagnosing the fault of the satellite attitude determination control system. First, Gaussian mixture model and the its traditional parameter estimation algorithm are reviewed. The component-wise expectation-maximization algorithm is used to estimate the parameters of Gaussian mixture model, which can lower the computational complexity of parameter estimation. Moreover, fault diagnosis, including detection and isolation, is carried out based on Gaussian mixture model, component-wise expectation maximization algorithm and k-means algorithm. Finally, the traditional method and our proposed method are applied for fault diagnosis on the satellite attitude determination control system. The simulation result shows that the new proposed method can, lower the computational complexity significantly, while the traditional and the new methods have nearly the same performance.