In Unmanned Aerial System (UAS) carrier landing, the target landing trajectory is significantly affected by deck motion. This paper proposes a precise carrier landing guidance method using Model Predictive Control (MPC) with deck motion prediction to achieve non-delayed tracking of the variable trajectory. Firstly, the linear time-varying forward position error dynamics of the aircraft and the aircraft carrier are established. Secondly, the deck motion prediction by the Auto-Regressive (AR) algorithm is used as known information in the MPC design to eliminate tracking lag, by predicting the error output. The cost function is transformed into a quadratic form, and the optimal control output is obtained using quadratic programming. Finally, numerical simulations with touchdown point distribution analysis are conducted to validate the performance of the carrier landing guidance algorithm.