Nano-graphene materials have improved many thermal properties based on polymer systems. The additive polymers’ thermal insulation cannot be significantly increased for use as a reinforcement in multifunctional thermally insulating polymer foam. Herein, we present the development of far-infrared emissivity and antistatic properties using multifunctional nano-graphene polyester fibers. Nano-graphene far-infrared thermal insulation polyester was synthesized with 2% nano-graphene and dispersant polypropylene wax-maleic anhydride (PP wax-MA) using the Taguchi method combined with grey relational analysis (GRA) to improve the thermal properties and the performance of the polymer composite. The thermogravimetric analysis (TGA) shows that the pyrolysis temperature of spinning-grade polyester was increased when the nano-graphene powder was added to the polyester. The differential scanning calorimeter (DSC) analysis confirmed the modification of polyester by nano-graphene, showing the effect of the nucleating agent, which ultimately improved the performance of the polyester. The physical properties of the optimized polyester fibers were improved with a yarn count of 76.5 d, tensile strength of 3.3 g/d, and an elongation at break increased from 23.5% to 26.7% compared with unmodified polymer yarn. These far-infrared emission rates increased from 78% to 83%, whereas the far-infrared temperature increased from 4.0 °C to 22 °C, and the surface resistance increased to 108 Ω. The performance of the optimized modified polyester yarn is far better than single-polypropylene-grafted maleic anhydride yarn. The performance of optimized modified polyester yarn, further confirmed using grey correlation analysis (GRA), can improve the yarns’ mechanical properties and far-infrared functions. Our findings provide an alternative route for developing nano-graphene polyester fabrics suitable for the fabric industry.