To address the increasing complexity and frequency of cybersecurity incidents emphasized by the recent cybersecurity threat reports with over 10 billion instances, cyber threat intelligence (CTI) plays a critical role in the modern cybersecurity landscape by offering the insights required to understand and combat the constantly evolving nature of cyber threats. Inspired by the powerful capability of large language models (LLMs) in handling complex tasks, in this paper, we introduce a framework to benchmark, elicit, and improve cybersecurity incident analysis and response abilities in LLMs for Security Events (SEvenLLM). Specifically, we create a high-quality bilingual instruction corpus by crawling cybersecurity raw text from cybersecurity websites to overcome the lack of effective data for information extraction. Then, we design a pipeline to auto-select tasks from the tasks pool and convert the raw text into supervised corpora comprised of question and response. The instruction dataset SEvenLLM-Instruct is used to train cybersecurity LLMs with the multi-task learning objective (27 well-designed tasks) for augmenting the analysis of cybersecurity events. Extensive experiments in our curated benchmark (SEvenLLM-bench) demonstrate that SEvenLLM performs more sophisticated threat analysis and fortifies defenses against the evolving landscape of cyber threats.