Abstract: As one of the new technologies for the high-performance complex metal components, the additive manufacturing technology has been used in the aerospace, automotive industry, medical, and nuclear powder fields. The metal additive manufacturing processes involve the complex physical phenomena such as heat transfer, thermal, phase transition, and flow. Numerical simulation methods in the different scales and cross-scales combined with the experimental verification can realize the understanding, control, and optimization of the complex physical phenomena in the additive manufacturing process, which can provide the strong support for the forming of high-quality, high-precision, and high-performance metal components. The numerical simulation of metal additive manufacturing processes in the macro, mesoscopic, micro, and multi-scale was reviewed in this article. The numerical simulation methods of temperature field, thermal stress field, powder bed, molten pool flow, and solidification behavior process were described. Finally, the development trend of the numerical simulation methods for the additive manufacturing was prospected.