Composites based on polypropylene (PP) filled with short carbon fibers (CF) increasingly attract attention due to the combination of low cost, light weight, excellent mechanical properties and a high thermal conductivity. For such composites, material extrusion additive manufacturing (aka. Fused Filament Fabrication, FFF) provides a promising and cost-effective manufacturing technique. In addition, FFF is known to be a fabrication method that guarantees the flow-induced orientation of the short fibers even in complex 3D parts. We report the design and manufacturing of 3D-printed PP/CF composites and investigated the impact of the printing- and thus the CF-orientation on the mechanical properties and thermal conductivity. A strong anisotropy in terms of flexural and impact properties and thermal conductivity was observed for the printed parts. The thermal conductivity along the printing direction was found to be three times higher than perpendicular to that direction. The present work explores and quantifies the anisotropic behavior of high performance thermoplastic composites and, thus, provides a key to the fabrication of customized parts with tailored and orientation-dependent properties.