Fused deposition modeling (FDM) is one of the additive manufacturing (AM) methods widely used in many divisions, especially medical implants and aerospace, due to capabilities to build complex 3D objects and geometries. However, quality and dimensional accuracy of the FDM parts are significantly influenced by the various FDM process parameters including filament wire material. In the present work, new filament wire material Thermoplastic Polyurethane (TPU) was utilized to produce FDM parts. Hence, deciding the optimum process parameters is very critical to produce the FDM parts with good surface quality (Ra) and dimensional accuracy (Δd) concurrently using TPU material. In this paper, the author has contributed to determine the optimum 3D printing process parameters to improve the quality and accuracy for the new filament wire material Thermoplastic Polyurethane (TPU) using multi-attribute decision making (MADM) methods namely Gray Relational Analysis (GRA) and technique for order preference by similarity to ideal solution (TOPSIS). Further, the results of GRA and TOPSIS techniques were compared and concluded that TOPSIS method substantially reduced the surface roughness to a value of 12% contrast to the GRA method whereas the dimensional deviation accuracy increased to 6.25% over the GRA method.