This paper proposed a new approach to estimate the abundance of each endmember at each pixel using distance geometry concepts and distance geometry constraints. It improves current hyperspectral unmixing algorithms in several aspects. Firstly, denoting the distance relationship with Cayley-Menger matrix makes it easy to calculate the barycentric coordinates of observation pixels, and the computation is independent of number of bands. Secondly, by the distance geometry constraint, the geometric structure of dataset is considered to obtain the optimal result with least geometric deformation. The synthetic and real data experimental results demonstrate that this algorithm is a fast and accurate algorithm for the hyperspectral unmixing.