Cutting brittle materials such as ceramics and glass by lasers or traditional saw method, costly fractures and associated damage such as chips and cracks can result. In most cases, these problems were caused as a result of the stress was not controlled properly and exceeded the critical value of the fracture. In this study, a dual-laser-bearn method was proposed to avoid fractures in glass laser cutting, where an off-focused CO2-laser beam was scanning on the top surface of glass periodically and repeatedly and a preheated-band which has a proper temperature was built. This preheated-band will reduce the temperature gradients when the glass is cut by the focused CO2-laser beam. Under these conditions, glass can be cut with melting method without any fractures. The process of cutting glass by dual CO2-laser beams was simulated numerically with FEA method and the distribution of temperature and thermal stress was investigated. The relationships between the cutting parameters, such as laser beam diameter, laser power, cutting speed, and the profile of the cutting groove were also discussed. The result showed that thermal stress decreased with the increasing width of preheated-banding, and the smaller the diameter of laser beam, the better the quality of the cutting groove was in the same laser power situation.