Time delay estimation (TDE) is an important issue in signal processing. Conventional TDE algorithms are usually efficient under white noise environments. In this paper, a joint noise reduction and -norm minimization method is presented to enhance TDE in colored noise. An improved subspace method for colored noise reduction is first performed. Then the time delay is estimated by using an -norm minimization method. Because the clean speech signal form the noisy signal is well extracted by noise reduction and the -norm minimization method is robust, the TDE accuracy can be enhanced. Experiment results confirm that the proposed joint estimation method obtains more accurate TDE than several conventional algorithms in colored noise, especially in the case of low signal-to-noise ratio.