Nonplanar 3D printing is a recently emerged approach to increase surface quality and part strength in additive manufacturing. In this paper, the impact of a nonplanar printing method utilized for the fused filament fabrication (FFF) technique on the resultant surface roughness of printed parts is presented. In particular, the influence of different inclination angles and part orientation on the obtainable surface quality was investigated by comparing a traditional planar printing strategy with a nonplanar finishing solution. A pyramidal geometry was utilized to assess the effect of inclination angle as well as part orientation and relative printhead movement on the surface characteristics. The results show a decrease in obtainable surface roughness for inclination angles up to 25°, while higher angles cause rougher surfaces when compared with results of planar 3D printing strategy. This can be explained by the way the nonplanar nozzle movements interact with previously deposited filament strands by deforming them due to the size of the nozzle and geometry of the 3D printed part. As a consequence, solutions for an improved nonplanar printing technique using Delta FFF printers are suggested that will be investigated in the future work.