Hyperspectral image classification (HSI classification) aims to assign land cover categories to pixels based on their spectral characteristics and has wide applications in environmental monitoring, smart agriculture, military operations, and other fields. However, in practical scenarios, the data distribution of the source and the target domain may be significantly different, that is, domain shift. Unsupervised domain adaptation (UDA) for HSI classification attempts to leverage the representation ability of source-trained models on the target domain. Various factors can cause a domain shift in HSI images. For example, different sensor characteristics and environmental factors can cause discrepancies in the data distribution, which can lead to different characteristics of the same object in different domains, making it difficult for a source-trained model to generalize well on target domains. To address this issue, huge progress has been made in existing methods. However, there are still two main problems: Firstly, existing methods usually only utilize adversarial learning mechanisms for feature alignment, ignoring the effectiveness of combining multiple learning strategies. Secondly, adversarial learning still has limitations in mitigating the representation tendency of source domain samples. To solve these two problems, we propose a hybrid training-driven unsupervised domain adaptation network (HT-UDANet) for HSI classification to improve adaptation performance on the target domain. Specifically, we first incorporate a self-training mechanism alongside adversarial learning to improve the model's compatibility from two different perspectives. Then, we further design a module-separated strategy in the self-training mechanism. With this strategy, the optimization process becomes more flexible and the high-quality pseudo-labels on target images can better suppress any possible overfitting on annotated source samples. Extensive experiments on multiple HSI datasets, including Pavia University, Pavia Center, Houston2013, and Houston2018 demonstrate the effectiveness of our proposed HT-UDANet for UDA HSI classification. A comparison with existing methods shows that HT-UDANet performs better in terms of classification accuracy.