An automatic gain control apparatus can prevent jumps in the gain coefficient when the gain coefficient is altered, due to a sharp change in the level of the received signal before and after the alteration. The apparatus includes a mean square circuit for processing the received signal, a gain coefficient generating circuit for generating a gain coefficient, a decision circuit for deciding whether the received level of the received signal has changed, and a control circuit for, when a change in the received level of the received signal is detected, determining a number of mean square values and a generating interval. The apparatus further includes a gain coefficient linear smoother for altering the gain coefficient over an interval, and a multiplier for multiplying the received signal by the gain coefficient obtained from the gain coefficient linear smoother.