This study uses machine learning, specifically transfer learning with neural networks, to improve the predictions of fission barrier heights and ground state binding energies of superheavy nuclei, which are crucial for calculating survival probabilities in fusion reactions. Transfer learning for neural networks involve two stages: pre-training and fine-tuning, each utilizing a distinct pre-training dataset and target dataset. In this work, we split the pre-training data into 60% for training and 40% for validation, while the target data are partitioned into 20% for test, with the remaining 80% further divided into 60% for training and 40% for validation. To construct the neural-network model, we adopt the proton number Z and mass number A as the input layer, employ two hidden layers, each containing 128 neurons with rectified linear unit (ReLU) activation, and set the learning rate to 0.001. For the fission-barrier-height model, the pre-training dataset is either the FRLDM or the WS4 model data, with the experimental measurements serving as the target set. For the ground-state binding-energy model, we first calculate the residuals between WS4 predictions and the AME2020 evaluation, then divide these residuals into a light-nucleus subset and a heavy-nucleus subset according to proton number. The light-nucleus subset is used for pre-training, and the heavy-nucleus subset for fine-tuning. After optimization, the root-mean-square error (RMSE) of the FRLDM barrier model decreases from 1.03 MeV to 0.60 MeV, and that of the WS4 barrier model drops from 0.97 MeV to 0.61 MeV. For the binding-energy model, the RMSE decreases from 0.33 MeV to 0.17 MeV on the test set and from 0.29 MeV to 0.26 MeV on the full data set. We also present the performances of the fission-barrier model before and after refinement, together with the predicted barrier heights along the isotopic chains of the new elements Z = 119 and Z = 120, and analyze the reasons for the differences in the results obtained by different models. We hope that these results will serve as a useful reference for future theoretical studies.