Climate indices generally contain nonstationary oscillations (NSO). Not much study has been done in the literature to reproduce the NSO processes through a stochastic time series model. Therefore, we proposed a model that reproduces the NSO of climate indices employing EMD- NSO resampling (NSOR) technique. The proposed simulation model was tested with three climate indices (i.e. AO, ENSO, and PDO) for the annual and winter (January, February, and March - JFM) datasets. The results of the proposed model are compared with the ones of the Contemporaneous Shifting Mean and Contemporaneous Autoregressive Moving Average (CSM-CARMA) model. One set of the 5000 year records is simulated from each model. The results (ex. Figure 1) indicated that the proposed model is superior to the CSM-CARMA model for reproducing the NSO process while the other basic statistics are comparatively well preserved in both models.