With the capability to build components with freeform geometries, laser powder bed fusion (L-PBF) is considered as one of the most promising techniques for industrial applications. Compared to conventional manufacturing technologies, an additional advantage of l-PBF process is the capability to fabricate parts with multiple materials, such as in-situ alloying and functionally graded alloys. In this regard, here we present a computational model to simulate the l-PBF of multiple materials. Based on volume of fluid (VOF) methods and computational fluid dynamics (CFD), the multi-physics multi-material model was successfully implemented with various physics of l-PBF process, including surface tension, Marangoni shear force, recoil pressure, compositional diffusion, etc. In addition, we demonstrated the numerical algorithm of ray tracing heat source for multiple materials. With reasonable assumptions, conduction mode or keyhole mode laser melting of miscible materials can be simulated via the proposed computational framework. Furthermore, such multi-physics model is capable of simulating l-PBF of an arbitrary number of materials. The computational model can help achieve insightful understanding of the l-PBF of multiple materials.