With the rapid development of photoelectric products, their miniaturization and high integration have intensified the problem of heat dissipation. Vapor chamber is a special type of heat pipe that is a particularly effective heat spreader for electronics. In this paper, a novel Leaf-vein-inspired Gradient Porous (LGP) wick structure is designed macroscopically and the LGP design is verified using a general model. After that, the gradient porous design Model 1G is selected for the subsequent mesoscopic modeling. Then a connected 2D random LGP wick model presenting porosity gradient is generated by the expanded quartet structure generation set method. Using the mesoscopic Lattice Boltzmann Method (LBM), the flow and heat transfer in the LGP wick model is analyzed. For verification, FLUENT based on the macroscopic finite volume method is used as a benchmark. Finally, the microscopic flow behaviors in the 2D random LGP wick model are analyzed using the LBM developed. Observing the entire flowing process from the inlet to outlet, it is possible to explain the mesoscopic and macroscopic phenomena well based on the microscopic flow behaviors.