In the system of Taiwan, if the demand function is given, then the Central Bank can improve economic growth and steady price by controlling the money supply. In fact, true money demand is unknown, so focal point of my paper is to estimate trading money demand function of Taiwan. First, I get that real income, real M1B, and nominal rate are integrated of order 1 processes by using Augmented Dickey-Fuller test (ADF test) , Phillips-Perron test (PP test) , and Ng-Perron (NP test) . In the conventional model of Engle and Granger (1987) , I use Johansen¡¦s (1988, 1991) maximun likelihood method to estimate co-integrating vector. The result is the same with Ching-Nun Lee (1996) . In the conventional model of Engle and Granger, a linear combination of individually I(1) series becomes I(0). Series have cointegration, but their linear combination is not I(0). Therefore the conventional model of Engle and Granger does not encompass all non-stational economic models. Harris, McCabe, and Leybourne (2002) provided the stochastic cointegration. The stochastic cointegration allows that a linear combination of individually I(1) series is not I(0). Therefore, my paper also uses stochastic cointegration to test trading money demand of Taiwan. The result is real M1B, real income, and one month rate have stochastic cointegration.