A continuous variable gain amplifier includes an attenuator network, a boost network, a first amplifying network, and a second amplifying network, where the attenuator network generates first differential output signals according to an input signal and sends the first differential output signals to the first amplifying network and the second amplifying network; the first amplifying network and the second amplifying network receive one output of the first differential output signals each, and generate a first final output signal and a second final output signal respectively according to an externally input control voltage; and the boost network receives the first final output signal and the second final output signal, generates second differential output signals, and sends a first output and a second output of the second differential output signals to the first amplifying network and the second amplifying network, respectively.