The total le ast squares (TLS) approximation estimates a parameter matrix from a linear model considering errors in both the observation vector [WTHX]L[WTBZ] and the dat a matrix [WTHX]A.[WTBZ] The TLS theory is more rigorous than the standard least squ ares . If some columns of [WTHX]A[WTBZ] can be known exactly, the problem is defined as the mixe d least squares—TLS problem. An iterative algorithm is derived to solve the LS TL S problem by using the principle of indirect adjustment. Compared with the method based on singular value decomposition(SVD) QR decompositon, the iterative algorithm coincides with the SVD algorithm. The calculated example proves that the ite rative algorithm is valid and rational.