This theses which uses Stock Price index compiled by the Taiwan Stock Exchanges for the period starting from February 1962 and ending at July 2007 as target for investment purpose, conducts simulation analyses aiming to determine the optimal investment holding period in Taiwan. In the process of simulation the frequency representing the optimal investment period is obtained to form a frequency distribution table. Based upon the optimal investing period frequency distribution and associated statistics the conclusion is drawn. Our finding has shown that a 24 months continuous holding period is the best among the alternatives ranging from 1 to 24 periods in terms of the average rate of returns and the variances of the rate of returns.