This series study develops a multi-functional yarn with far-infrared emission, heating, and antistatic properties for winter clothing. In Part I, polyethylene terephthalate (PET) is used as the polymer matrix, and nano germanium powder is uniformly mixed with PET by the melt blending process for modification, in order that the PET composite has far-infrared function. Afterwards, the modified PET is made into 75d/72f fully drawn yarn (FDY) by melt spinning and melt drafting. The properties of the yarn, including tensile strength, elongation at break, yarn count (in denier), far-infrared emissivity, and far-infrared heating are discussed. In order to optimize the quality of yarn in the melt spinning process, this study designs process parameters consisting of germanium powder addition, melt temperature, mold temperature, nozzle temperature, gear pump speed, and take-up speed using the Taguchi method. Then, the analytic hierarchy process (AHP) is applied to obtain the weights of each quality, which will be used in the technique for order preference by similarity to an ideal solution (TOPSIS) to obtain the optimal processing parameters for multi-quality yarn. The results show that the tensile strength of the optimized modification PET yarn is 4.84 g/d, the elongation at break is 41.26%, yarn count is 74.39d/72f, the far-infrared emissivity is 89% and the far-infrared heating is 6.3℃. The properties of the optimized modified yarn are obviously better than general PET yarn.