In-channel amplitude noise and inter-channel amplitude mismatch are main factors limiting the performance of time-wavelength interleaved photonic analog-to-digital conversion (TWIPADC) system. An amplitude correction method based on adaptive noise cancellation principle for TWIPADC is proposed. In the scheme, the in-channel amplitude noise introduced by unstability of the laser source and optical time division multiplexing (OTDM) module is eliminated in real time by using the adaptive interference cancellation principle, while the inter-channel amplitude mismatch introduced by the wavelength division multiplexing module is corrected by adopting a calibration procedure. The structure of TWIPADC system based on the proposed correction scheme is presented. The proposed amplitude correction principle and procedure are analyzed theoretically by building the corresponding mathematical model. The simulation results show that the amplitude noise of TWIPADC caused by optical source and OTDM module can be eliminated in real time effectively by the proposed adaptive cancellation scheme. The signal-to-noise-and-distortion ratio of a 32 GS/s TWIPADC system with 16-channel can be improved more than 30 dB by using the proposed amplitude correction method.