Laser cutting process plays a key role in obtaining accurate parts in Laminated Solid Manufacture. Conventional laser cutting machine adopts motion control scheme. For further improving the cutting accuracy, dynamic factors are to be taken into account. The dynamic compensation scheme is proposed. The method combines the advantages of close-loop position control and computed torque control. Different from other presented schemes, the method is not model-based. A multilayer neural network is employed to realize the inverse mechanic dynamics. The complicated dynamic parameter identification problem becomes the learning process under supervision. Experiments have been conducted to verify the proposed method for improving the laser cutting accuracy.