Cognitive biases are systematic deviations in thinking that lead to irrational judgments and problematic decision-making, extensively studied across various fields. Recently, large language models (LLMs) have shown advanced understanding capabilities but may inherit human biases from their training data. While social biases in LLMs have been well-studied, cognitive biases have received less attention, with existing research focusing on specific scenarios. The broader impact of cognitive biases on LLMs in various decision-making contexts remains underexplored. We investigated whether LLMs are influenced by the threshold priming effect in relevance judgments, a core task and widely-discussed research topic in the Information Retrieval (IR) coummunity. The priming effect occurs when exposure to certain stimuli unconsciously affects subsequent behavior and decisions. Our experiment employed 10 topics from the TREC 2019 Deep Learning passage track collection, and tested AI judgments under different document relevance scores, batch lengths, and LLM models, including GPT-3.5, GPT-4, LLaMa2-13B and LLaMa2-70B. Results showed that LLMs tend to give lower scores to later documents if earlier ones have high relevance, and vice versa, regardless of the combination and model used. Our finding demonstrates that LLM%u2019s judgments, similar to human judgments, are also influenced by threshold priming biases, and suggests that researchers and system engineers should take into account potential human-like cognitive biases in designing, evaluating, and auditing LLMs in IR tasks and beyond.