Disclosed are a digital predistortion system and a method used for amplifying signals. A multi-band digital predistortion system comprises a multi-band input signal, at least a power amplifier, input aliasing logic, a feedback signal exported from amplification output, and predistortion logic responding to aliasing images. Each frequency band uses spaced frequency as center, and the bandwidth of each frequency band is basically smaller than the frequency space among the frequency bands. The power amplifier is used to provide amplification output including distortion performance. The input aliasing logic is used to generate an aliasing image of each frequency band. The aliasing image of the first frequency band is in a Nyquist zone, and the aliasing image of the second frequency band is in another Nyquist zone. The Nyquist zone and each of the other Nyquist zones have width of half of the sampling frequency of the input signal. The feedback signal comprises expression of at least a part of the predistortion performance. The predistortion logic is used to generate a predistortion factor which makes the output of the power amplifier linearized.