In this paper, we propose a time-difference-of-arrival (TDOA) based outdoor localization approach using a deep neural network (DNN) with a novel weighted mean squared error (WMSE) loss. The weight is determined aided by the Cramer-Rao lower bound (CRLB) of localization accuracy. A training set rebalancing strategy is proposed to approximate the WMSE loss with the classical MSE loss and make the training process efficient, without the need of collecting more training samples. Extensive numerical investigations of ideal and nonideal scenarios are included to examine the effectiveness of the proposed approach.