Laser welding of transparent materials, including glasses, established in the recent years. This study reports the results of the theoretical with experimental validation to transient temperature and stress fields on bonding small glass pieces to solder glass by laser welding. A 3D finite element model of bonding small glass pieces to solder glass by laser welding is developed and validated with experimental micro-structural analysis. An influence of laser average power and welding speed on the temperature field and stress field during welding is studied. A range of average laser power and welding speed, with a standard of the appropriate temperatures and ultimate stresses of sealing during laser welding, are determined. The results show that in the range of laser average power of 45~75 W and welding speed of 1–2 mm/s, the heat source central temperature increases with an increase of laser average power or the decrease of welding speed, and the corresponding maximum temperature exceeds 650 °C. The maximum transient thermal stress is calculated to be 152 MPa, it appeared at the boundary of the upper glass interface. The boundary stress at the front end of the heat source and the transient thermal stress at the inflection point are larger than the transient thermal stress at the middle point. The experimental and theoretical results show that the melting layer has excellent morphology and mechanical properties at the average laser power of 65 W and welding speed of 90 mm/min, which is applicable for the bonding of small glass pieces to solder glass by laser welding.