In this study, experimental investigations regarding the heat transfer performance of an evaporator with capillary wick are presented. The capillary wick structure is composed of sintered multilayer copper mesh. The multilayer copper mesh was sintered on the copper plate. With different combinations of mesh screens, the wick thickness of mesh 140 ranged from 0.6 to 1.0 mm, and those of meshes 60 and 140/60 were both 1.0 mm. The operating pressures used in this study were 0.86 × 105, 0.91 × 105, 0.96 × 105, 1.01 × 105, and 2.0 × 105 Pa. The experimental results indicate that the heat transfer performance was strongly dependent on the thickness of the sintered mesh structure and on the mesh size. The operating pressure also has a strong influence on the evaporation/boiling heat transfer performance of a mesh structure sintered using a single mesh size. However, it was also observed that the evaporation/boiling heat coefficient increased with an increase in the thickness of the capillary wick structure, which is less than 1.0 mm. The experimental results further illustrate that the composite sintered mesh structure was capable of properly enhancing the heat transfer performance, especially under high pressure. The maximum enhancement was 31.98%.