Leveled reading (LR) aims to automatically classify texts by the cognitive levels of readers, which is fundamental in providing appropriate reading materials regarding different reading capabilities. However, most state-of-the-art LR methods rely on the availability of copious annotated resources, which prevents their adaptation to low-resource languages like Chinese. In our work, to tackle LR in Chinese, we explore how different language transfer methods perform on English-Chinese LR. Specifically, we focus on adversarial training and cross-lingual pre-training method to transfer the LR knowledge learned from annotated data in the resource-rich English language to Chinese. For evaluation, we first introduce the age-based standard to align datasets with different leveling standards. Then we conduct experiments in both zero-shot and few-shot settings. Comparing these two methods, quantitative and qualitative evaluations show that the cross-lingual pre-training method effectively captures the language-invariant features between English and Chinese. We conduct analysis to propose further improvement in cross-lingual LR.