The Tandem Neural Network Architecture (TNNA) algorithm was an inversion framework through reverse mapping. Its reliability strongly depended on accurate surrogate modeling within the true posterior region of parameters. For reactive transport problems, establishing a globally accurate surrogate model required a large number of numerical model samples, which considerably limited the efficiency of inversion processes. To address this challenge, the TNNA-AUS-MF inversion method was proposed, in which the original TNNA was integrated with a multi-fidelity (MF) surrogate model and an adaptive updating sampling (AUS) strategy. In this method, multi-fidelity surrogate models were iteratively established based on the conventional TNNA and local samples to update the inversion results. The proposed algorithm was validated using a hypothetical cation-exchange experiment. By controlling the number of initial surrogate model samples, six scenarios with different initial surrogate model accuracies were designed. The results showed that the TNNA-AUS-MF significantly reduced the number of forward simulations while yielding more reliable inversion results compared with the TNNA method. Furthermore, it was demonstrated that the neural network could establish nonlinear relationships between low- and high-fidelity models, and that incorporating the adaptive updating sampling strategy effectively enhanced the performance of the inversion algorithm.