Periodic or quasi-periodic phenomena reveal intrinsic characteristics in various natural processes, such as weather patterns, movement behaviors, traffic flows, and biological signals. Given that these phenomena span multiple modalities, the capabilities of Multimodal Large Language Models (MLLMs) offer promising potential to effectively capture and understand their complex nature. However, current MLLMs struggle with periodic tasks due to limitations in: 1) lack of temporal modelling and 2) conflict between short and long periods. This paper introduces Period-LLM, a multimodal large language model designed to enhance the performance of periodic tasks across various modalities, and constructs a benchmark of various difficulty for evaluating the cross-modal periodic capabilities of large models. Specially, We adopt an Easy to Hard Generalization" paradigm, starting with relatively simple text-based tasks and progressing to more complex visual and multimodal tasks, ensuring that the model gradually builds robust periodic reasoning capabilities. Additionally, we propose a Resisting Logical Oblivion optimization strategy to maintain periodic reasoning abilities during semantic alignment. Extensive experiments demonstrate the superiority of the proposed Period-LLM over existing MLLMs in periodic tasks. The code will be available on GitHub.