The characteristic of layer-wise addition of selective laser melting (SLM) process leads to the anisotropy, especially reflecting in mechanical performance. In this work, the textures and thermal conductivities of an SLM-processed Cu-Ni-Si alloy were measured along the horizontal and vertical directions to establish the relationship between crystallographic texture and thermal anisotropy for the first time. Results show that the vertical plane reveals columnar grains with stronger (100) preferred orientations and the content of high-angle grain boundaries (HAGBs) is 64.6%, while for the horizontal plane, the equiaxed-like grains with (100), (101) and (111) orientations exist equally and the content of HAGBs is 52.7%. The thermal conductivity along the vertical direction (187.83 ± 0.72 W/m K) is much higher than that along the horizontal direction (62.86 ± 0.60 W/m K) at room temperature, indicating a strong thermal anisotropy. The thermal anisotropy can be ascribed to the grain shapes, orientations and HAGBs, which affect the grain boundary scattering extent of electron and phonon transport. The findings would be a valuable reference for tailoring thermal conductivity of SLM-processed alloys in the future.