The optimal stopping time is of profound significance in statistics, mathematics and finance, and can be used to derive optimal choices from uncertain problems such as volatile golden market. The paper mainly focuses on studying the problem of optimal stopping time by using the basic theory of Brownian motion and resolving the optimal time node for trading gold at a specified time in which tendency of golden price is known. Brownian motion, one of the basic theories in the stock market, solves probabilistic random problems and helps calculate the time node closet for best-selling time in formula. This paper uses Brownian motion as a research method to calculate optimal stopping time. Then the data of golden price is selected from 2021 to 2022 as a model and used for analysing boundary and retracement state of specific golden price to determine the optimal stopping time that maximal trading revenue generates. Therefore, this paper provides a common method to study best stopping time in bull market to derive the optimal profit. The empirical results verify the feasibility and operability of the optimal stopping time model in the investment market. Investors can use boundary value and retracement value as reference data to sell gold in time in order to avoid huge losses. Investors can also adjust the parameters of the model according to their own investment strategies, so that the calculated results of the model can meet individual needs.