The inflation rate, which measured using consumer price index, can be separated into a combination of two persistent and temporary components. This separating is particularly important in analyzing inflation rate and policies to control it. In fact, without knowing the persistent component of inflation, called core inflation, quantitative targeting of inflation may not be accurate. Core inflation as a more persistent component can be measured stripping out the transitory movements in prices. The understanding of the behavior of the national core inflation rate series needs to understand provincial core inflation since the construction of the former is based on the provincial series. So, the purpose of this paper is the estimation of provincial and national core inflation in Iran. Core inflation is unobservable variable, so it estimated using Space State Model and Kalman Filter. Results show that average core inflation in all of the provinces, as well as Iran, is less than average underlying inflation. The standard deviation of core inflation in some provinces is more than underlying inflation. While core inflation in other provinces, as well as Iran, has more standard deviation as compared to underlying inflation.