Laser cutting liquid crystal display (LCD)-glass is a complex process of interaction between laser and material. In thermal cracking method laser cutting, the size of the crack tip stress intensity factor (SIF) decides whether the crack extends in the whole cutting process. The size of the crack tip SIF during cutting process is calculated using thermal weight function, comparing with the fracture criterion judges the crack′s extension situation. The effects of laser power, spot radius, the cutting speed and crack length on the crack tip SIF are studied. It is concluded that the greater the laser power, the smaller the cutting speed, and the smaller the spot radius, the faster the crack tip SIF increaseing the bigger the peak value. Under different crack lengths, the crack tip SIF increase speed and the peak value are also different. The experimental verification illustrates the feasibility of this technology.