Due to the high dimensionality of hyperspectral images, dimensionality reduction is usually performed before target detection. Principal component analysis and maximum noise components are two of the most classical and commonly used dimensionality reduction methods in hyperspectral image processing. They use image variance and signaltonoise ratio as indices to reduce the dimensionality of hyperspectral images,which are used to measure secondorder statistic information. Therefore, the small target may be discarded after being reduced by this kind of methods due to its characteristics. The principal kurtosis analysis algorithm based on the highorder statistic characteristics of data can solve these problems well. This algorithm can extract the information about small targets which cannot be maintained after dimensionality reduction based on secondorder statistic information. However, the principal kurtosis analysis algorithm has a slow convergence speed. Therefore, an improved principal kurtosis analysis algorithm is proposed. It can improve the convergence speed and reduce the iteration times of principal kurtosis analysis. Simulation results show that the proposed algorithm can shorten the computation time and improve the convergence speed.