A steel pipe drawing apparatus, which can manufacture a drawn steel pipe which is a long object with high accuracy and at high speed as well as improves dimensional accuracy of respective thick-wall portions and cutting positions of the drawn steel pipe, is realized. When a stepped drawn steel pipe is manufactured by moving a die and a plug relatively in the same direction as a steel pipe drawing direction and in an opposite direction thereto, a first hydraulic cylinder moves the die relatively in a direction corresponding to the steel pipe drawing direction, and a second hydraulic cylinder moves the plug relatively in a direction opposite to a moving direction of the die. At this time, a position detecting sensor detects a stroke position of the second hydraulic cylinder, and a computer receives positional information detected by the position detecting sensor and controls a moving velocity of the second hydraulic cylinder. Thereby, the computer makes a moving velocity v2 of the second hydraulic cylinder higher than a moving velocity v1 thereof in “b” region based upon a position detecting signal in “d” region. Therefore, the drawn steel pipe is drawn at the higher moving velocity v2 so that no sag occurs in a wall-thickness gradient in the “d” region.