As one of the various attempts to reduce the size of display bezel, high-precision glass cutting process is required to be developed for future displays. In this study, the Bessel-beam Laser Cutting (BLC) process has been studied, which is capable of minimizing the thermal deformation of the black matrix (BM) material on glass. In an experimental setup composed of IR ps laser with bessel-beam optics, the smallest thermal degradation of BM and the highest cutting precision are achieved as 40µm and 10µm, respectively. When reducing thermal effects caused by high-order beams without sacrificing glass breaking strength, effective heat affected zone (HAZ) could be reduced near by 30um width from the cutting line. This high precision cutting technology will contribute to realize extremely narrow bezel display near future.