The invention provides a down-hole hammer power head of a rotary drilling rig and the rotary drilling rig. The down-hole hammer power head comprises a power supply box (43) and a screw rod (30). The power supply box (43) comprises a box body and a rotation hub which is arranged in the box body and outputs rotation power. The rotation hub is used for driving a down-hole hammer (20). The upper end of the screw rod (30) is connected with the rotation hub in a driving mode, and the lower end of the screw rod (30) is used for connecting with the down-hole hammer (20). A down-hole hammer function is added to the rotary drilling rig so that construction ability of the rotary drilling rig is enlarged, especially for hard lithosphere which can be chiseled by using the down-hole hammer function of the rotary drilling rig, and then the rotary drilling rig can drill into the hard lithosphere, so that the ability of drilling into the hard lithosphere of the rotary drilling rig is greatly improved.