Ensemble empirical mode decomposition (EEMD) and least squares linear fitting (LSLF) are applied to estimate the historical trends of surface air temperature (SAT) from observations and Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations during the period 1901–2005. The magnitudes of trends estimated by the two approaches are comparable. The trend calculated by the EEMD approach is larger than that by the LSLF approach in most (23/27) of the models during 1901–2005. During the slow warming period, the EEMD trend is smaller than the LSLF trend. The root-mean-square errors (RMSEs) between the raw and reconstructed times series by the LSLF approach are larger than those by the EEMD trend component and multi-decadal variability components during 1901–2005 in most of the models and observations. During 1901–70 (or 1971–2005), the RMSEs between the raw and reconstructed times series by LSLF are larger than those by the EEMD trend component. In this sense, the EEMD trend is a better choice to obtain the climate trends in observations and CMIP5 models, especially for short time periods. This is because the trend estimated by LSLF cannot capture the internal variability and the cooling in some years. The estimated global warming rates (trend) are consistently larger (smaller) than those from observations in 11 of 27 CMIP5 models during 1901–2005 in the slow and rapid warming periods. This implies these 11 models have consistent responses to greenhouse gases for any period.