This paper proposes a new dynamic event trigger adaptive horizon-based interval predictor-model free robust predictive control (IP-MFARPC) method for hovercraft heading tracking control problem without precise modeling under disturbance. Firstly, based on the input-output (I/O) data from the past period, we use partial form dynamic linearization (PFDL) to establish an online data model for the hovercraft, which is more accurate than the compact form dynamic linearization (CFDL) method. Secondly, the proposed method uses interval observers and predictors (IO&IP) to solve the prediction model offline and uses online rolling optimization to solve the optimal control sequence. During the solution process, the offline prediction model is utilized, and LMI is employed to transform robust L2 gain constraints, enhancing the control method's anti-interference ability and the accuracy of the rolling optimization process. Additionally, dynamic event triggering and adaptive prediction step mechanisms are introduced to improve online solving speed without compromising control performance. Finally, simulation results demonstrate that the IP-MFRAPC method effectively tracks the variable heading of the hovercraft under disturbances, offering faster solving times compared to methods without these mechanisms.