As a novel additive manufacturing technique, laser powder bed fusion (LPBF) provides a new forming method for the fabrication of divertor mono-block for the future nuclear fusion reactor. In this study, pure tungsten samples were built by the LPBF technique horizontally and vertically. It is found that under the heat load of 15 MW/m2, there were severe melting and sputtering in the vertically built samples, while only a little cracking and sputtering occured in the horizontally built samples. It is believed that the anisotropy of the thermal conductivity in LPBFed tungsten samples is caused by the microstructure difference in different directions. For the horizontally built sample, the direction of the heat flow is parallel to the building direction, and the coarse columnar grains grown along this direction is favorable for heat conduction. For the vertically built sample, the heat flow direction is perpendicular to the building direction, grain boundariesand the crack network would hinder the heat conduction. Therefore, the heat accumulated on the surface of vertically built sample could cause melting. This study shows that the building direction has an unavoidable impact on the fabrication of divertor mono-block using the LPBF technique.