Abstract In this paper, a novel adaptive time delay estimation (TDE) method under the existence of amplitude attenuation is proposed for the impulsive noise environment. We present a closed form of the recursive solution for the TDE by using the maximum correntropy criterion (MCC). First, a two-step TDE method, which has the advantage of simplicity, is proposed. In this approach, the coefficients in the noncausal finite impulse response (FIR) filter are employed to model the time delay. Furthermore, to improve the robustness of the proposed two-step algorithm, a closed form of the recursive solution for the direct TDE is proposed, which does not have any free parameter, as in the two-step algorithm in gradient-based techniques. Finally, the convergence property regarding the direct TDE algorithm is performed.