A communication method and a system for converging a fifth generation (5G) communication system for supporting higher data rates beyond a fourth generation (4G) system with a technology for internet of things (IoT) are provided. A terminal and a base station and communication method of the same are provided. The method includes receiving, from a base station (BS), configuration information of discontinuous reception (DRX), performing beam measurement before a start of an on duration of the DRX, transmitting, to the BS, beam feedback information according to the beam measurement result, and performing a certain operation after transmitting the beam feedback information.