Abstract We investigate the interconnectedness and spillovers between oil price inflation and CPI inflation in the G7 countries and China over the available period 1987M6-2020M6. To this end, we employ the multivariate DECO-GARCH model and both time-domain and frequency-domain spillover methods to achieve the objectives. We find that there is a reasonably high degree of integration between the oil price inflation and the CPI inflation rates in those countries. This relationship is not only time-varying, but also has been rising over time and, remarkably so, during oil crises and financial stress episodes. We also show that the oil price inflation is a crucial transmitter of spillovers to the CPI inflation of the countries under consideration, particularly to the US inflation, which, in turn, has a weak to mild influence on the paths of inflation of other countries. Additionally, the largest gross directional spillovers to other CPI inflation rates accrue to the US, while the lowest accrue to China. Finally, the oil price inflation influences the CPI inflation over the short-end of the business cycle, but much less so over the medium- to long-ends.