With the impressive performance in various downstream tasks, large language models (LLMs) have been widely integrated into production pipelines, like recruitment and recommendation systems. A known issue of models trained on natural language data is the presence of human biases, which can impact the fairness of the system. This paper investigates LLMs' behavior with respect to gender stereotypes, in the context of occupation decision making. Our framework is designed to investigate and quantify the presence of gender stereotypes in LLMs' behavior via multi-round question answering. Inspired by prior works, we construct a dataset by leveraging a standard occupation classification knowledge base released by authoritative agencies. We tested three LLMs (RoBERTa-large, GPT-3.5-turbo, and Llama2-70b-chat) and found that all models exhibit gender stereotypes analogous to human biases, but with different preferences. The distinct preferences of GPT-3.5-turbo and Llama2-70b-chat may imply the current alignment methods are insufficient for debiasing and could introduce new biases contradicting the traditional gender stereotypes.