Using distance geometry concepts and distance geometry constraints, this paper proposes a new abundance estimation method for hyperspectral unmixing, which improves current hyperspectral unmixing algorithms in several aspects. Firstly, considering the geometric structure of dataset by the distance geometry constraint, the optimal result with least geometric deformation can be obtained. Secondly, the Cayley-Menger matrix is introduced to denote the pairwise distances between the observation pixels and endmembers, which make it easy to calculate the barycentric coordinates and the computation is independent of number of bands. A series of synthetic and real data experimental results demonstrate that this algorithm is an accurate and fast algorithm for the hyperspectral unmixing.