Abstract: Based on the minimal residual criterion, a relaxtion method is proposed to improve the convergence efficiency of the barycentre method for solving the distance equations. The relaxation factor for adaptive selecting the iterative step of barycentre method is derived by the minimum residual criterion. The proposed method has the advantages of simple iterative format without the matrix inversion and to simplify the procedure without calculating the Hessian matrix. Finally, the novel method is performed to solve the data of GNSS and marine positioning examples to show its performance, and results show the numerical convergence experiments are performed to show the convergence efficiency improvment.