The utility model provides a bonding head driving device and a bonding device. The bonding head driving device comprises a rack, a first damping mechanism, a second damping mechanism, a first translation mechanism and a second translation mechanism. The first translation mechanism comprises a first sliding rail, a first driving module, a first sliding seat and a second sliding rail, the first sliding rail is arranged in the first horizontal direction, the first sliding seat is connected to the first sliding rail, the first driving module is arranged on the first vibration reduction mechanism and connected with the first sliding seat, and the second sliding rail is arranged on the first sliding seat in the second horizontal direction. The second translation mechanism comprises a third sliding rail, a second driving module, a second sliding seat and a fourth sliding rail, the third sliding rail is arranged in the second horizontal direction, the second sliding seat is connected to the third sliding rail, the second driving module is arranged on the second vibration reduction mechanism and connected with the second sliding seat, and the fourth sliding rail is arranged on the second sliding seat in the first horizontal direction. The second slide rail and the fourth slide rail are slidably connected with the bonding head. The vibration of the bonding head can be reduced, and the bonding precision is improved.