A method and an apparatus are provided for estimating and removing interference of a signal at a wireless repeater operating in a multi-carrier system. In the method, a current echo channel linear prediction coefficient, which represents a coefficient between a current train signal section and a previous train signal section, is estimated using a current echo channel coefficient estimated in the current train signal section and a previous echo channel coefficient generated in the previous train signal section. A next echo channel coefficient is estimated using the current echo channel coefficient, the previous echo channel coefficient, and the current echo channel linear prediction coefficient. An echo channel coefficient outside a train signal section is estimated using the current echo channel coefficient and the next echo channel coefficient.