Large Language Models (LLMs) have recently achieved remarkable performance in long-context understanding. However, current long-context LLM benchmarks are limited by rigid context length, labor-intensive annotation, and the pressing challenge of label leakage issues during LLM training. Therefore, we propose \textsc{AcademicEval}, a live benchmark for evaluating LLMs over long-context generation tasks. \textsc{AcademicEval} adopts papers on arXiv to introduce several academic writing tasks with long-context inputs, \textit{i.e.}, \textsc{Title}, \textsc{Abstract}, \textsc{Introduction}, and \textsc{Related Work}, which cover a wide range of abstraction levels and require no manual labeling. Moreover, \textsc{AcademicEval} integrates high-quality and expert-curated few-shot demonstrations from a collected co-author graph to enable flexible context length. Especially, \textsc{AcademicEval} features an efficient live evaluation, ensuring no label leakage. We conduct a holistic evaluation on \textsc{AcademicEval}, and the results illustrate that LLMs perform poorly on tasks with hierarchical abstraction levels and tend to struggle with long few-shot demonstrations, highlighting the challenge of our benchmark. Through experimental analysis, we also reveal some insights for enhancing LLMs' long-context modeling capabilities. Code is available at https://github.com/ulab-uiuc/AcademicEval