Neural network positioning technology, as one of the mainstream in indoor Wi-Fi positioning systems, is playing an increasingly important role in location-based services. The main challenge is that the samples are prone to be outdated as the indoor environment changes or the wireless signal varies over time, i.e., the samples’ Age of Information (AoI) is large, which leads to the trained model not being available. However, recollecting data to retrain the model is both time-consuming and labor-intensive. To address the above problem, this article proposes a fast adaptation approach based on Bayesian meta-learning that makes the pretrained model acquire a learned learning capability so that it can quickly learn new tasks based on the acquisition of existing knowledge. Specifically, first, a model-agnostic learning scheme is introduced to guide the learning process, which could automatically learn the optimal model parameters and hyperparameter settings. Second, to mitigate the effects of model uncertainty, especially to prevent the overfitting situation based on a limited number of samples, we combine the Stein variational gradient descent (SVGD) with the model-agnostic learning scheme, i.e., Bayesian meta-learning. Compared with traditional meta-learning algorithms, the proposed method makes the training more robust by inferring the Bayesian posterior from a probabilistic perspective. Extensive experimental results show that the proposed approach effectively overcomes the impact of large AoI on localization performance while decreasing labor consumption significantly.