Abstract: Accurate groundwater modeling is essential for the scientific management and decision-making of groundwater resources, as it involves hydraulic conductivity, a key hydrogeological parameter. To fully understand and effectively utilize groundwater, we not only need to accurately estimate the spatial distribution of hydraulic conductivity but also need to quantify the uncertainty of the parameter to evaluate its credibility. In this study, parameter inversion and uncertainty analysis of hydraulic conductivity were investigated using the Bayesian Convolutional Neural Network（BCNN）. To test the validity of the method, a synthetic numerical experiment of a two-dimensional steady-state hydraulic tomography pumping test was conducted. The baseline model is a convolutional neural network with an encoder-decoder structure, which builds an inverse mapping that estimates the parameter field directly from the head fields obtained by spatial interpolation. Based on this deterministic model, we trained the Bayesian Convolutional Neural Network. The results show that the BCNN outperforms the deterministic model in accuracy under various training data sizes, with a more significant advantage when the data is scarce. By analyzing the test set samples, we observe that the models exhibit different levels of confidence for their estimates across different regions. A well-trained BCNN can faithfully capture the approximate pattern of the hydraulic conductivity distribution. Moreover, the BCNN also excels in estimating the more challenging multimodal non-Gaussian logarithmic hydraulic conductivity field compared to the generative model, which indicates the wide applicability of the BCNN under diverse geological media conditions. The use of Bayesian Convolutional Neural Networks enables accurate inversion of hydraulic conductivity and evaluating uncertainty, providing a solid basis for subsequent physical processes such as groundwater flow simulation.