In this paper, a novel 3D laser cutting numerical model is developed based on the lattice Boltzmann method, providing a new approach to simulate this process numerically. The proposed model consists of two parts: (i) a thermal enthalpy based solid-liquid phase change model is applied to simulate the melting phenomenon occurring on the solid work piece; (ii) a pseudo-potential model is incorporated to take into consideration the interaction between the environmental gas and the molten material. This newly developed model is validated by comparing results of simulated cutting kerf width with existing experimental data of 304 stainless steel thin plates. The changing shapes of the melt film on the cutting front under different cutting conditions are shown. Performances of laser cutting on a work piece are evaluated for different Peclet number, dimensionless laser power, dimensionless line energy, and dimensionless gas jet velocity. For a work piece with given thickness, cutting through conditions and cutting efficiency for different values of these dimensionless parameters are presented. (C) 2017 Elsevier Ltd. All rights reserved.