A method and apparatus for informing relaxed measurement upon early measurement reporting in a wireless communication system is provided. A wireless device evaluates the at least one of the relaxed measurement conditions based on measurement results of the serving frequency. A wireless device performs relaxed measurement on the serving frequency and/or the at least one of neighbor frequencies based on the evaluation. A wireless device transmits, to the network, a message including 1) measurement results on each frequency of the frequency set, and 2) information on the relaxed measurement on the each frequency of the frequency set.