Accurate state of health (SOH) estimation of lithium-ion batteries is critical for maintaining reliable and safe working conditions for electric vehicles (EVs). The machine learning-based method with health features (HFs) is encouraging for health prognostics. However, the machine learning method assumes that the training and testing data have the same distribution, which restricts its application for different types of batteries. Thus, in this paper, a deep learning neural network and fine-tuning-based transfer learning strategy are proposed for accurate and robust SOH estimation toward different types of batteries. First, a universal HF extraction strategy is proposed to obtain four highly related HFs. Second, a deep learning neural network consisting of long short-term memory (LSTM) and fully connected layers is established to model the relationship between the HFs and SOH. Third, the fine-tuning-based transfer learning strategy is exploited for SOH estimation of various types of batteries. The proposed methods are comprehensively verified using three open-source datasets. Experimental results show that the proposed deep learning neural network with the HFs can estimate the SOH accurately in a single dataset without using the transfer learning strategy where the mean absolute error (MAE) and root mean square error (RMSE) are constrained to 1.21% and 1.83%. For the transfer learning between different aging datasets, the overall MAE and RMSE are limited to 1.09% and 1.41%, demonstrating the reliability of the fine-tuning strategy.