Approximately 40% of patients admitted to the medical intensive care unit (ICU) require mechanical ventilation. An accurate prediction of successful extubation in patients is a key clinical problem in ICU due to the fact that the successful extubation is highly associated with prolonged ICU stay. The prolonged ICU stay is also associated with increasing cost and mortality rate in healthcare system. This study is retrospective in the aspect of ICU. Hence, a total of 41 patients were selected from the largest academic medical center in Taiwan. Our experimental results show that predicting successful rate of 87.8% is obtained from the proposed predicting function. Based on several types of statistics analysis, including logistic regression analysis, discriminant analysis, and bootstrap method, three major successful extubation predictors, namely, rapid shallow breathing index, respiratory rate, and minute ventilation, are revealed. The prediction of successful extubation function is proposed for patients, ICU, physicians, and hospital for reference.