We present a neural network for mitigating pseudorange bias to improve localization performance with data collected from Android smartphones. We represent pseudorange bias using a pragmatic satellite-wise Multiple Layer Perceptron (MLP), the inputs of which are six satellite-receiver-context-related features derived from Android raw Global Navigation Satellite System (GNSS) measurements. To supervise the training process, we carefully calculate the target values of pseudorange bias using location ground truth and smoothing techniques and optimize a loss function containing the estimation residuals of smartphone clock bias. During the inference process, we employ model-based localization engines to compute locations with pseudoranges corrected by the neural network. Consequently, this hybrid pipeline can attend to both pseudorange bias and noise. We evaluate the framework on an open dataset and consider four application scenarios for investigating fingerprinting and cross-trace localization in rural and urban areas. Extensive experiments demonstrate that the proposed framework outperforms model-based and state-of-the-art data-driven approaches.