Spectral unmixing is one of the important techniques for hyperspectral data processing. The analysis of spectral mixing is often based on a linear, fully constrained (FC) (i.e., nonnegative and sum-to-one mixture proportions), and least squares criterion. However, the traditional iterative processing of FC least squares (FCLS) linear spectral mixture analysis (LSMA) (FCLS-LSMA) is of heavy computational burden. Recently developed geometric LSMA methods decreased the complexity to some degree, but how to further reduce the computational burden and completely meet the FCLS criterion of minimizing the unmixing residual needs to be explored. In this paper, a simple distance measure is proposed, and then, a new geometric FCLS-LSMA method is constructed based on the distance measure. The method is in line with the FCLS criterion, free of iteration and dimension reduction, and with very low complexity. Experimental results show that the proposed method can obtain the same optimal FCLS solution as the traditional iteration-based FCLS-LSMA, and it is much faster than the existing spectral unmixing methods, particularly the traditional iteration-based method.