With the broadband signal, weak signal energy and small magnitude in comparison with the tradition MT, the long-period magnetotelluric survey has a higher data processing requirement. In this paper, the Robust algorithm based on repeated median estimator was applied to long-period magnetotelluric impedance tensor estimates. Compared with the Robust maximum likelihood estimate (M estimate), the repeated median estimator has no need of reset parameters in data processing, and can increase the estimate of the breakdown point up to 50% and get an unbiased estimate of impedance tensor. An application example shows that the Robust algorithm based on repeated median estimator has a strong advantage in the solution of the impedance tensor.