This paper deals with the demand for money, including narrow money (M1) and broad money (M2) in China. We use the cointegration and error-correction model to formulate the function of money demand and merge the short-run and long-run equations to give forecasts over different horizons. In particular, we combine very simple artificial neural networks (ANNs) with the cointegration and error-correction model to give a nonlinear model. These models are quarterly models, sampled from the first quarter of 1980 to the fourth quarter of 1994, and the multi-step forecasts are from the first quarter of 1990 to the fourth quarter of 1994. Both the fitted values and predictive values for M1 and M2 are satisfactory. Finally, we give forecasts for M2 from the first quarter of 1995 to the second quarter of 1996.