Fast independent component analysis dimensionality reduction for hyperspectral image needs a large amount of matrix and iterative computation. By analyzing hotspots of the fast independent component analysis algorithm, such as covariance matrix calculation, white processing, ICA iteration and IC transformation, a GPU-oriented mapping scheme and the optimization strategy based on GPU-oriented algorithm on memory accessing and computationcommunication overlapping were proposed. The performance impact of thread-block size was also investigated. Experimental results show that better performance was obtained when dealing with the hyperspectral image dimensionality reduction problem: the GPU-oriented fast independent component analysis algorithm can reach a speedup of 72 times than the sequential code on CPU, and it runs 4～6.5 times faster than the case when using a 16-core CPU. 