The paper analyzes inflation targeting which used in many countries as a tool for the monetary policy of central banks. The study of the experience of inflation targeting over the past quarter century shows a number of shortcomings. The important one is that inflation targeting is powerless in relation to import inflation. This problem is particularly acute for import-dependent countries. The authors summarize the failure of inflation targeting to influence the import of inflation regarding inflation caused by the increase in production costs. The problem is studied by the example of post-communist Georgia (that uses inflation targeting) and its major trading partners. The authors analyze various modifications of the inflation indicator, such as agflation, munflation, and imflation. It is shown that the first two reflect price fluctuations on the nutrition, medical care, medication and utilities. Imflation reflects the dynamics of import prices on the domestic market, in the formation of which the exchange rate of the national currency is of great importance. The indicators of agflation and munflation together with the traditional indicator of inflation should become one of the important macroeconomic indicators for governments that develop economic and social policies. The authors propose a new approach to monetary policy, called complex inflation targeting. In this case, monetary policy targets are not only inflation, but also imflation. As for the exchange rate of the national currency, it should be influenced by the actual level of the imflation indicator.