An innovative multi-layer coating method has been developing for the production of graded refractive index lenses by repeated peripheral coating of a core fiber of higher refractive index with polymer solutions of progressively lower refractive indices. In this work, optimum operational conditions were investigated for the production of the core fiber of high refractive index by melt spinning technique. Favorable extrusion temperatures were determined by visual observation of the melt fracture in the extruded strands. The variance of the fiber diameter depended markedly on both the die temperature at the exit of the extruder and the chimney temperature of the fiber cooling section. In order to remove the small amount of oligomer contained in the copolymer, a vent was installed at the middle of the extruder to continuously evaporate the oligomer during extrusion. At an optimum melting temperature, the oligomer could be well removed without any loss of the polymer melts from the vent.