A variable gain amplifier includes an amplifying circuit and a gain adjusting circuit including the following circuits. A linear exponential transforming circuit transforms a linear controlling signal to output an exponential controlling signal. A voltage buffer circuit is coupled with the linear exponential transforming circuit to receive the exponential controlling signal, outputs a feedback signal to a power transforming circuit, and outputs a voltage controlling signal to control a gain of the amplifying circuit according to the exponential controlling signal and a bias current. A power transforming circuit is coupled with the linear exponential transforming circuit and the voltage buffer circuit to receive the exponential controlling signal and the feedback signal and take two times of a square root of a product of the exponential controlling signal and the feedback signal plus the bias current to output a power signal to the linear exponential transforming circuit.