Robust turbo equalization over discrete time channels with inter-symbol interference (ISI) in the presence of channel uncertainties is investigated. The turbo equalization framework proposed in this paper contains a linear equalizer (LE) and a trellis based decoder. In this framework, a minimax scheme and a competitive scheme are studied, which incorporate the uncertainty in channel information into equalizer design in order to improve robustness. The validation of the performance improvement gained by the proposed algorithms are demonstrated through simulations.