As a blind source separation (BSS) process, independent component analysis (ICA) has recently been used in hyperspectral imagery (HSI) unmixing. It models a "mixed" pixel as a linear mixture of the constituent (endmember) spectra weighted by the correspondent abundance fractions. However, the unmixing results of ICA are not satisfied. In this paper, a complexity based BSS algorithm called complexity pursuit is introduced. Compared to the other BSS techniques, this algorithm has two major advantages. First, it does not ignore signal structure. Second, the impact of noise can be largely reduced. In addition, an improved conjecture is proposed which makes complexity pursuit suitable for HSI unmixing. The experimental results show that complexity pursuit provides a promising approach to unmix HSI. Keywords: complexity pursuit, independent component analysis, hyperspectral imagery unmixing