Streamflow of the Murray River (MR) was investigated from 1978 to 2017, using statistical analysis based on Indian Ocean modes of variability. During the cool season, June to August (JJA), observations and reanalysis products have been used to analyse the relation of streamflow of MR with Indian Ocean High (IOH) and Southern Annular Mode (SAM) over South Australia (SA). Recently, the river has suffered from severe drought, whereas drought drivers differ significantly in terms of interannual and decadal timescales. As a defining feature of atmospheric general circulation, the IOH is quantitatively simulated in all global climate models. Variations in the streamflow of MR have been linked to the variability of intensity and positions of Indian Ocean high pressure (IOHP) meridionally and the impact of SAM across the Indian Ocean. It is found that the correlation of streamflow with IOHP is (r = -0.41), SAM (r = -0.52) and shows the strongest correlation with Indian Ocean High Longitude (IOHLN), which is -0.56. Moreover, SAM explains only 27% of streamflow variability, while IOHP and IOHLN indices calculated by the Center of Action (COA) approach explain 39% of the variation. This paper examines the decline of the inflow rate of MR in SA by applying the COA approach, Mann-Kendall (MK) test and Pearson correlation. We further investigate the impact of significant predictors over the flow of MR. Inflow rate of the hydrology of MR is influenced by the period of time, which shows a decreasing trend with -1.976 by applying autocorrelation. Overall, monthly and annual streamflows have also investigated a significant decreasing trend. Cross-correlation is also used to verify the relationship between streamflow and significant predictors of MR.