This paper’s purpose is to analyze the early exercise strategy of American options based on the binomial tree model. We use this binomial tree model to analyze the prices of American and European options to determine whether an American option should be exercised early under certain circumstances and to compare the price difference between the two options to calculate the premium. Options are common financial derivatives that have been traded in the financial markets for a long time. As a key tool for hedging, speculation, and enhancing portfolio strategies, options are integral to modern financial markets, which attract a large number of researchers to make research on option pricing. However, in current academic research, there is insufficient investigation into the differences between American put options and European put options, particularly regarding their exercisable time. Therefore, this paper will mainly explore the optimal exercise time for put options using a two-period binomial model, which can help investors make better decisions to seek maximum profit.