Fused Filament Fabrication (FFF) process has lower surface roughness quality, precision and it takes longer to fabricate compared to the conventional manufacturing operations and some additive manufacturing technologies. In order to overcome these issues, a rotary extruder head with a nozzle having a rectangular orifice has been utilized in this work. A new tool path planning for a rectangular nozzle is designed to increase the efficiency of the extrusion process by this nozzle. As a result, finer features (such as outer surfaces, edges, corners, etc.) can be 3D-printed with greater accuracy, and inner regions can be extruded in less time. The design algorithms for outer shells, inner regions, and infill paths are presented here to show the procedure of the tool path planning and examined for different test cases. Some modifications in the case of concave curves as the outer shells are also offered. Moreover, these test cases have been fabricated in our hybrid manufacturing system named HYBRO, which has five axes plus milling and rotary extruder heads to demonstrate this new strategy. The results demonstrate the smallest and the largest bead widths obtained with the same rectangular nozzle.