In this work, we study the inflation targeting effect on the inflation dynamics in the case of four industrial countries. Our objective is to check whether the inflation targeting policy (ITP) has a significant impact on the change of the inflation path. We use a non-parametric approach that doesn’t require any previous modelling. This is the evolutionary spectral analysis, as defined by Priestley (1965-1996). Then, we use a test that can detect many break points on the time series. This test is inspired by Subba Rao (1981). We use an extension to this test to allow the detection of multiple breaks. We base this on the extension of Ahamada and Boutahar (2002). This is the first time that this method is used in the case of inflation-targeting countries. We find that the inflation-targeting policy had a transition period for countries that had a high and volatile inflation experience before the inflation-targeting adoption. There is the case of New Zealand, Canada and Sweden. In these countries, we identify a structural change in the inflation series resulting to the inflation targeting intervention. However, In the case of other countries like United Kingdom that have a relatively lower inflation rate experience before the ITP adoption, we didn’t find a break point caused by this monetary policy intervention. In this case, the ITP had a role of ensuring this price stability. This result is explained by the fact that the inflation targeting is relevant when the initial inflation to be stabilized is near the target range (Artus, 2004). So, in this paper we justify the intuition of Artus (2004). The second result in our paper consists on the nature of inflation stabilization during the inflation-targeting period. The results proof a long-term stabilization on the inflation dynamic in the period of IT. These results traduce the success of this new framework to anchor the inflation expectation anchoring. So, we can conclude that this policy is preferment to ensure price stability in the case of industrials countries.