Consider a 1-D backward heat conduction problem with Robin boundary condition. We recover u(x, 0) and u(x, to) for to ∈ (0, T) from the measured data u(x, T)respectively. The first problem is solved by the Morozov discrepancy principle for which a 3-order iteration procedure is applied to determine the regularizing parameter. For the second one, we combine the conditional stability with the Tikhonov regularization together to construct the regularizing solution for which the convergence rate is also established. Numerical results are given to show the validity of our inversion method