Abstract: In this paper, an adjustment model of minimizing the 1-norm of residuals and the1-norm of unknowns (hereafter, simply called the adjustment of minimizing the L-X1-norm) is first established as follows and then the average extreme point of the adjustment of minimizing the L-X 1-norm isdefined to solve the problem of uniqueness of the solution of minimizing the adjustmentof the L 1-norm. After that, the accuracy estimate of the adjustment of minimizing theL-X 1-norm (including the adjustment of minimizing the L 1-norm) is discussed. Fina-lly, the adjustment of minimizing the L-X 1-norm is applied to deformation analysis withmeasurements including gross errors.