A starting device of a gas internal combustion engine, the starting device being configured to perform slow air turning to rotate the gas internal combustion engine at a low speed before starting the internal combustion engine, the starting device comprising: a rotation-speed detection unit configured to detect a rotation speed of the gas internal combustion engine; a compressed-air tank; a compressed-air introduction unit configured to supply the compressed air from the compressed-air tank to each of the cylinders according to an order of an ignition timing of the gas internal combustion engine; a compressed-air supply unit configured to supply the compressed air from the compressed-air tank to the compressed-air introduction unit via a pilot air-pipe; and a control device; characterized by an orifice disposed in an air pipe between the compressed-air supply unit and the compressed-air introduction unit, the orifice being configured to restrict a flow rate of the compressed air introduced into the cylinders; wherein the compressed-air supply unit includes: a slow-air-turning main starting valve for delivering the compressed air from the compressed-air tank to the compressed-air introduction unit via the orifice; and a main starting valve for delivering the compressed air from the compressed air tank to the compressed air introduction unit; the control device includes a cumulative rotation-speed setting device configured to be capable of varying a threshold value of a cumulative rotation speed, the control device being configured to open the slow-air-turning main starting valve such that the gas internal combustion engine rotates at a low speed in order to check an inside of each of cylinders of the gas internal combustion engine and to secure lubrication between the cylinders and the pistons and to halt supply of the compressed air by the compressed-air supply unit by controlling a slow-air-turning electromagnetic valve configured to supply a pilot compressed air to the slow-air-turning main starting valve when the gas internal combustion engine reaches the set cumulative rotation speed on the basis of the rotation speed detected by the rotation-speed detection unit, such that when the gas internal combustion engine reaches the set threshold value of the cumulative rotation speed on the basis of the rotation speed detected by the rotation-speed detection unit, the slow-air-turning main starting valve is closed and the main starting valve is opened to increase the rotation speed to a rotation speed at which the gas internal combustion engine can be operated by fuel-gas ignition. a rotation-speed detection unit configured to detect a rotation speed of the gas internal combustion engine; a compressed-air tank; a compressed-air introduction unit configured to supply the compressed air from the compressed-air tank to each of the cylinders according to an order of an ignition timing of the gas internal combustion engine; a compressed-air supply unit configured to supply the compressed air from the compressed-air tank to the compressed-air introduction unit via a pilot air-pipe; and a control device; characterized by an orifice disposed in an air pipe between the compressed-air supply unit and the compressed-air introduction unit, the orifice being configured to restrict a flow rate of the compressed air introduced into the cylinders; wherein the compressed-air supply unit includes: a slow-air-turning main starting valve for delivering the compressed air from the compressed-air tank to the compressed-air introduction unit via the orifice; and a main starting valve for delivering the compressed air from the compressed air tank to the compressed air introduction unit; a slow-air-turning main starting valve for delivering the compressed air from the compressed-air tank to the compressed-air introduction unit via the orifice; and a main starting valve for delivering the compressed air from the compressed air tank to the compressed air introduction unit; the control device includes a cumulative rotation-speed setting device configured to be capable of varying a threshold value of a cumulative rotation speed, the control device being configured to open the slow-air-turning main starting valve such that the gas internal combustion engine rotates at a low speed in order to check an inside of each of cylinders of the gas internal combustion engine and to secure lubrication between the cylinders and the pistons and to halt supply of the compressed air by the compressed-air supply unit by controlling a slow-air-turning electromagnetic valve configured to supply a pilot compressed air to the slow-air-turning main starting valve when the gas internal combustion engine reaches the set cumulative rotation speed on the basis of the rotation speed detected by the rotation-speed detection unit, such that when the gas internal combustion engine reaches the set threshold value of the cumulative rotation speed on the basis of the rotation speed detected by the rotation-speed detection unit, the slow-air-turning main starting valve is closed and the main starting valve is opened to increase the rotation speed to a rotation speed at which the gas internal combustion engine can be operated by fuel-gas ignition.