This paper investigates the Granger causality between electricity consumption (EL) and economic growth for Taiwan during 1980-2007 using the cointegration and error-correction models. The results indicate that EL and real GDP are cointegrated, and that there is unidirectional short and long run Granger causality from economic growth to EL but not vice versa. Considering cointegrated property, this study proposes a new error-correction state space model (ECSTSP) with the error-correction term (ECT) in its state vector to forecast both EL and real GDP simultaneously, whereas the ECM is not in the state vector of classical state space model (STSP). The out-of-sample forecasting ability of the ECSTSP is compared with STSP and SARIMA models using six forecasting horizons from 1-year to 6-year. The results suggest that all of the models have strong forecasting performance with MAPE less than 5.4%, but the ECSTSPs have the smallest average values of MAPEs for both EL and GDP, which are 2.50% and 1.74%, respectively. For short-term predictions, SARIMA models are as good as STSP or ECSTSP ones. For long-term prediction, ECSTSP is the best model, because the cointegration relationship between real GDP and EL is taken into account in this model.