In the last years, hyperspectral analysis have been applied in many remote sensing applications. In fact, hyperspectral unmixing has been a challenging task in hyperspectral data exploitation. This process consists of three stages: (i) estimation of the number of pure spectral signatures or endmembers, (ii) automatic identification of the estimated endmembers, and (iii) estimation of the fractional abundance of each endmember in each pixel of the scene. However, unmixing algorithms can be computationally very expensive, a fact that compromises their use in applications under real-time constraints. In recent years, several techniques have been proposed to solve the aforementioned problem but until now, most works have focused on the second and third stages. The execution cost of the first stage is usually lower than the other stages. Indeed, it can be optional if we known a priori this estimation. However, its acceleration on parallel architectures is still an interesting and open problem. In this paper we have addressed this issue focusing on the GENE algorithm, a promising geometry-based proposal introduced in.1 We have evaluated our parallel implementation in terms of both accuracy and computational performance through Monte Carlo simulations for real and synthetic data experiments. Performance results on a modern GPU shows satisfactory 16x speedup factors, which allow us to expect that this method could meet real-time requirements on a fully operational unmixing chain.