This paper considers target localization using time delay (TD) and angle of arrival (AOA) measurements in distributed multiple-input multiple-output (MIMO) radar. Aiming at the problem that the localization performance of existing algorithms degrades sharply in the presence of impulsive noise, we propose a novel localization algorithm based on ℓ p -norm minimization and iteratively reweighted least squares (IRLS). Firstly, the TD and AOA measurement equations are established in the presence of zero-mean symmetric α-stable noise; then, the localization problem is transformed to a ℓ p -norm minimization problem by linearizing the measurement equations; and finally, the ℓ p -norm minimization problem is solved using IRLS by which the target position estimate is obtained, and the optimal choice of norm order p is deduced. Moreover, the Cramér–Rao bound (CRB) for target position estimation in impulsive noise is also derived, generalizing the Gaussian CRB. Simulation results demonstrate that the proposed algorithm outperforms existing algorithms in terms of localization accuracy and robustness in impulsive noise.