A clock synchronization apparatus and method, which perform clock synchronization by determining a clock offset and a network delay between a master and a slave in an IEEE 1588 system. The clock synchronization method and apparatus include observing a clock offset and a packet delay using a timing packet received from a master node; estimating a clock offset and a packet delay from the observed clock offset and the observed packet delay; and performing synchronization with the master node based on the clock offset and the packet delay.