The invention is a gas container valve fastening machine which comprises a column erected on a base, a clamp unit for securely supporting a gas container placed on the base in an upright posture parallel to the column, a rotary drive unit vertically movably disposed above clamp the unit along the column, a rotary transmission unit interlocked and connected to an output shaft of the rotary drive unit, and a wrench attached to a lower end of the rotary transmission unit. A valve engaged in the wrench is rotated by the rotary transmission unit and threaded into the screw hole of a sleeve of the gas container, including a guide rod arranged parallel to the column, and a movable frame with its middle portion attached to the guide rod to be free to move in the axial direction, and free to rotate in the circumferential direction via a bearing boss.