The convergence speed of the conventional adaptive LMS algorithms for time delay estimation (TDE) is highly dependent on the spectral distribution of the desired random source signals of interest, thus the performance of TDE might be degraded, dramatically. To solve this problem, in this letter, a DCT-transform domain constrained adaptive normalized-LMS filtering scheme, referred to as the adaptive constrained DCT-LMS algorithm, is devised for TDE. Computer simulation results verify that the proposed scheme can be used to achieve desired performance, for input random signals with different spectral distributions; it outperforms the unconstrained DCT-LMS and time-domain constrained adaptive LMS algorithms.