Ultra-Wide Band (UWB) microwave breast cancer detection is a promising new technology for routine physical examination and home monitoring. The existing microwave imaging algorithms for breast tumor detection are complex and the effect is still not ideal, due to the heterogeneity of breast tissue, skin reflection, and fibroglandular tissue reflection in backscatter signals. This study aims to develop a machine learning method to accurately locate breast tumor. A microwave-based breast tumor localization method is proposed by time-frequency feature extraction and neural network technology. First, the received microwave array signals are converted into representative and compact features by 4-level Discrete Wavelet Transform (DWT) and Principal Component Analysis (PCA). Then, the Genetic Algorithm-Neural Network (GA-NN) is developed to tune hyper-parameters of the neural network adaptively. The neural network embedded in the GA-NN algorithm is a four-layer architecture and 10-fold cross-validation is performed. Through the trained neural network, the tumor localization performance is evaluated on four datasets that are created by FDTD simulation method from 2-D MRI-derived breast models with varying tissue density, shape, and size. Each dataset consists of 1000 backscatter signals with different tumor positions, in which the ratio of training set to test set is 9:1. In order to verify the generalizability and scalability of the proposed method, the tumor localization performance is also tested on a 3-D breast model. For these 2-D breast models with unknown tumor locations, the evaluation results show that the proposed method has small location errors, which are 0.6076mm, 3.0813mm, 2.0798mm, and 3.2988mm, respectively, and high accuracy, which is 99%, 80%, 94%, and 85%, respectively. Furthermore, the location error and the prediction accuracy of the 3-D breast model are 3.3896mm and 81%. These evaluation results demonstrate that the proposed machine learning method is effective and accurate for microwave breast tumor localization. The traditional microwave-based breast cancer detection method is to reconstruct the entire breast image to highlight the tumor. Compared with the traditional method, our proposed method can directly get the breast tumor location by applying neural network to the received microwave array signals, and circumvent any complicated image reconstruction processing.