A two-dimensional based integrated predictive iterative learning control(2D-IPILC) method is applied to the point-to-point tracking problem with the trajectory updating strategy. The 2D-IPILC method can fully take advantages of the freedom brought by the untracked points, and can improve the capability of dealing with the disturbance in the time domain by combining the feature of model predictive control. As time-varying parameters are involoved in the updating trajectory scheme, the model of the 2D-IPILC method is also time-varying. Therefore, the characteristics of time-varying transition matrix and full reponse are analyzed in detail. Furthermore, the convergence principle and conditions of the 2D-IPILC method are proved based on the 2D theory, and the effects of the control parameter setting are also discussed. The 2D-IPILC method can get faster convergence than the fixed trajectory methods, and is more robust than the direct optimization algorithm. Finally, these advantages are demonstrated by numerical simulation.