Over the last two decades, the residential building sector has been one of the largest energy consumption sectors in New Zealand. The relationship between that sector and household energy consumption should be carefully studied in order to optimize the energy consumption structure and satisfy energy demands. Researchers have made efforts in this field; however, few have concentrated on the association between household energy use and the cost of residential buildings. This study examined the correlation between household energy use and residential building cost. Analysis of the data indicates that they are significantly correlated. Hence, this study proposes time series methods, including the exponential smoothing method and the autoregressive integrated moving average (ARIMA) model for forecasting residential building costs of five categories of residential buildings (one-storey house, two-storey house, townhouse, residential apartment and retirement village building) in New Zealand. Moreover, the artificial neutral networks (ANNs) model was used to forecast the future usage of three types of household energy (electricity, gas and petrol) using the residential building costs. The t-test was used to validate the effectiveness of the obtained ANN models. The results indicate that the ANN models can generate acceptable forecasts. The primary contributions of this paper are twofold: (1) Identify the close correlation between household energy use and residential building costs; (2) provide a new clue for optimizing energy management.