A new method of explicitly adaptive time delay estimation (EATDE) algorithm is proposed for estimating a varying time delay parameter. The proposed method is based on the Haar wavelet transform of cross-correlations. The proposed algorithm can be viewed as a gradient-based optimization of lowpass filtered cross-correlations, but requires less computational power. The algorithm shows a global convergence property for wide-band signals with uncorrelated noises. A convergence analysis including mean behavior, mean-square-error behavior, and steady-state error of delay estimate is given. Simulation results are also provided to demonstrate the performance of the proposed algorithm.