The processing parameters of soda-lime glass cutting with several nanosecond 532 nm pulsed fiber laser are studied in order to obtain sufficiently large ablation rate and better processing quality. The influences of laser processing parameters on effective cutting speed and cutting quality of 1~2 mm thick soda-lime glass are studied. The experimental results show that larger laser pulse energy will lead to higher effective cutting speed and larger maximum edge collapse of the front side of the glass samples. Compared with that of 1.1 mm thick glass samples, the 2.0 mm thick glass samples is more difficult to cut. With the pulse energy of 51.2 μJ, the maximum edge collapse is more than 200 μm for the 2.0 mm thick glass samples. In order to achieve the high effective cutting speed and good cutting quality at the same time, the dual energy overlapping method is used to obtain the better cutting performance for the 2.0 mm thick glass samples, and the cutting speed of 194 mm/s and the maximum edge collapse of less than 132 μm are realized.