Core inflation is meant to distinguish the permanent long run trend of the inflation rate from its transitory movements. This paper makes an attempt to estimate core inflation for Zambia using the exclusion method and the limited influence estimators' method. The prices of the items in the Consumer Price Index (CPI) basket for the period 1986 to 2008 were used to estimate the core inflation. The computed indicators seem to show lower inflation than the headline CPI inflation rate. The results need to be tested for stability and for biasness from the headline inflation. However, the computed core inflation gives a guide to what core inflation for Zambia is.