A servo-driven cylinder screen printing machine being used with a feeder and a printed sheet collecting unit to perform printing on printing material sheets, comprising: a machine frame including an infeed table mounted in a front portion of the machine frame to form a feeding zone and connected to the feeder, a delivery table mounted in a rear portion of the machine frame to form a delivering zone and connected to the printed sheet collecting unit, the delivery table including a first conveyor located adjacent to the printed sheet collecting unit, and the first conveyor being connected to and brought by a first driving motor to generate a first conveying speed the same as a synchronous speed of the printed sheet collecting unit, and a second conveyor being connected to and brought by a second driving motor to generate a second conveying speed that is properly changeable and adjustable according to a speed of a print cylinder or the delivery table, and a printing zone formed between the feeding zone and the delivering zone; the print cylinder being installed in the printing zone and having a rotary shaft and a cylinder body mounted on the rotary shaft, the second conveyor located between the first conveyor and the print cylinder; at least one direct-drive servo mechanism being connected to an end of the rotary shaft of the print cylinder to form a direct-drive device for driving the rotary shaft and accordingly the cylinder body to rotate at precisely controlled rotational speed; a screen carrier being located above the printing zone of the machine frame and adjacent to a surface of the cylinder body of the print cylinder; and at least one linear servo mechanism being connected to the screen carrier to form another direct-drive device for driving the screen carrier to linearly move above the machine frame; wherein the print cylinder is driven by the direct-drive servo mechanism to rotate steplessly in one direction for performing alternate and successive stop and print movements, and the screen carrier is driven by the at least one linear servo mechanism to move for working with the print cylinder in performing printing operation with high accuracy in synchronization. a machine frame including an infeed table mounted in a front portion of the machine frame to form a feeding zone and connected to the feeder, a delivery table mounted in a rear portion of the machine frame to form a delivering zone and connected to the printed sheet collecting unit, the delivery table including a first conveyor located adjacent to the printed sheet collecting unit, and the first conveyor being connected to and brought by a first driving motor to generate a first conveying speed the same as a synchronous speed of the printed sheet collecting unit, and a second conveyor being connected to and brought by a second driving motor to generate a second conveying speed that is properly changeable and adjustable according to a speed of a print cylinder or the delivery table, and a printing zone formed between the feeding zone and the delivering zone; the print cylinder being installed in the printing zone and having a rotary shaft and a cylinder body mounted on the rotary shaft, the second conveyor located between the first conveyor and the print cylinder; at least one direct-drive servo mechanism being connected to an end of the rotary shaft of the print cylinder to form a direct-drive device for driving the rotary shaft and accordingly the cylinder body to rotate at precisely controlled rotational speed; a screen carrier being located above the printing zone of the machine frame and adjacent to a surface of the cylinder body of the print cylinder; and at least one linear servo mechanism being connected to the screen carrier to form another direct-drive device for driving the screen carrier to linearly move above the machine frame; wherein the print cylinder is driven by the direct-drive servo mechanism to rotate steplessly in one direction for performing alternate and successive stop and print movements, and the screen carrier is driven by the at least one linear servo mechanism to move for working with the print cylinder in performing printing operation with high accuracy in synchronization.