Model predictive control (MPC) has become more attractive in control engineering for the last decades because of its efficiency and robustness. In this paper, an effective control strategy is proposed for vibration reduction of mechanical flexible systems in which establishment of a global dynamic model of the controlled system is not necessary. A modified model-free adaptive predictive controller is designed by combination of MPC and model-free control theory. The novel idea of this contribution is that by using the compact-form dynamic linearization technique, the upcoming system outputs within a specified prediction horizon can be predicted in sequence. The data-based prediction model of the system only requires input/output information, and therefore the future control input increments as well as the unknown system parameters called pseudo-jacobian matrix can be estimated. To improve parameter estimation accuracy, another online estimation method namely recursive least-squares algorithm is applied instead of using the conventional projection algorithm. The control performance is verified nummerically for vibration control of a flexible ship-mounted crane represented as a multi-input multi-output (MIMO) system. Simulation results indicate that significant reduction of the crane oscillations and better control performance are observed when using the proposed controller in comparison with other traditional methods.