A circuit with programmable signal bandwidth is provided. The circuit includes a first charge and discharge device, a first reset device, and a first variable capacitor device. The first reset device is coupled to the first charge and discharge device, and the first variable capacitor device is coupled to the first charge and discharge device. The first reset device is controlled by a discharge enable signal and used to provide a first discharge path. When the discharge enable signal turns off the first reset device, the first variable capacitor device generates a first total equivalent capacitor to the first charge and discharge device according to n reference signals, and n is an integer greater than 0.