As large language models (LLMs) gradually become integral tools for problem solving in daily life worldwide, understanding linguistic inequality is becoming increasingly important. Existing research has primarily focused on static analyses that assess the disparities in the existing knowledge and capabilities of LLMs across languages. However, LLMs are continuously evolving, acquiring new knowledge to generate up-to-date, domain-specific responses. Investigating linguistic inequalities within this dynamic process is, therefore, also essential. In this paper, we explore inequalities in new knowledge learning by LLMs across different languages and four key dimensions: effectiveness, transferability, prioritization, and robustness. Through extensive experiments under two settings (in-context learning and fine-tuning) using both proprietary and open-source models, we demonstrate that low-resource languages consistently face disadvantages across all four dimensions. By shedding light on these disparities, we aim to raise awareness of linguistic inequalities in LLMs' new knowledge learning, fostering the development of more inclusive and equitable future LLMs.