An end-member extraction method for spectral unmixing that is based on Particle Swarm Optimization (PSO) is developed and presented in this paper. The objective function minimized by PSO is the volume of the simplex containing the hyperspectral vectors, following the geometrical characteristics inherent to the data sets. The proposed algorithm has been successfully applied to synthetic hyperspectral image sets, showing to be very fast and be able to determine a high number of endmembers. The experimental results of the proposed algorithm are encouraging. The performance of different versions of PSO is also investigated.