Automated story generation has been one of the long-standing challenges in NLP. Among all dimensions of stories, suspense is very common in human-written stories but relatively under-explored in AI-generated stories. While recent advances in large language models (LLMs) have greatly promoted language generation in general, state-of-the-art LLMs are still unreliable when it comes to suspenseful story generation. We propose a novel iterative-prompting-based planning method that is grounded in two theoretical foundations of story suspense from cognitive psychology and narratology. This theory-grounded method works in a fully zero-shot manner and does not rely on any supervised story corpora. To the best of our knowledge, this paper is the first attempt at suspenseful story generation with LLMs. Extensive human evaluations of the generated suspenseful stories demonstrate the effectiveness of our method.