In this paper, a mathematical model for performance prediction of a high-speed planing hull in forward acceleration motion has been developed. Three degrees of freedom have been considered for solving the problem. Utilizing previous empirical equations of displacement ships, motion of the vessel in displacement regime has been simulated. In order to model pre-planing and planing regimes, 2D + T theory has been used. Equations for prediction of performance of a surface piercing propeller (SPP) and an engine have been presented. Validity of the proposed method has been assessed by comparing its results against previous experimental data, and good agreement between experimental and mathematical results in prediction of performance of planing hulls has been seen. Motion of the vessel has been simulated under the action of a semi-submersible propeller and an outboard engine. Behavior of the vessel has been analyzed and the relationships between forces and moments with displacements, as well as pitch and heave rate have been described. It has shown how hydrodynamic force contributes as the beam Froude Number goes beyond 1.0, which results in increment of vertical position of the vessel. Also, it has been observed that, net pitching moment decreases from a positive value to a negative value in displacement regime, and then, by the appearance of hydrodynamic moment, net moment approaches zero and finally vanishes. The results also have indicated that a sudden jump occurs in thrust force vs. time curve, which is caused at critical advanced ratio. Beside this, it has been seen that, when propeller comes of water, a sharp increase in advanced ratio happens. Effects of surge motion have also been studied, which show that, maximum trim angle occurs at a larger beam Froude Number. It has also been observed that sinkage is larger in the presence of surge motion in pre-planing regime as extra hydrodynamic forces due to damping and added mass contributions in vertical direction occur. Finally, it has been observed that surge is accompanied with larger resistance which is resulted due to contribution of heave and pitch motions in surge direction, especially in pre-planing and planing regimes.