The ultrashort pulse laser, which has a wide application prospect, can weld the glass directly. It does not need to add the absorbing medium between the two pieces of glass and does not need thermal treatment for the material. The welding of two pieces of fused silica is successfully achieved using the thermal accumulation effect of femtosecond laser pulses. In addition, the dependence of welding quality on laser repetition frequency and power is investigated. The welding zone of fused silica comprises three parts, e.g., the circular cavity on the top, the molten area in the middle and the linear damage structure at the bottom, and all the three parts make contributions to the welding strength of fused silica. The experiments show that with a laser repetition frequency of 500 kHz, the molten zone area increases with the increase of the laser power, but the welding strength increases first and then decreases. When the laser power keeps as 4.14 W, both molten zone area and welding strength decrease with the increase of laser repetition frequency. Furthermore, two pieces of aluminosilicate glass and soda-lime glass are also successfully welded and the welding end surface morphologies of the glass with different components are compared.