Abstract: To more briefly calculate the accurate solution of the hanging-point motion parameters of the beam-pumping unit,the walking beam's swing equation according to the geometry relationship and movement characteristic of the four pitmen mechanism in the beam-pumping unit is found.Due to this equation,he gets the variation rules of the walking beam's swing angle and the calculation formula of the distance,velocity and accelaration in the hanging-point movement.Thereby,he gives a method to calculate the accurate solution of the hanging-point motin parameters of the beam-pumping unit.In the case of CYJ10-3-37HB pumping unit,he calculates its hanging-point movement parameters,and gives out the comparing curves between the simple harmonic motion and the crankmovinglump-mechanism motion which is simplified.The analysis indicates that the position of the hanging-point's top and down center is not where the crank angle is 180° and 360° (or 0°) which is known conventionally,so negative value appears when it is calculated as convention.For this reason,he gives out the method to determine the position of movement limit,and he draws the conclusion that the top and down centre position of CYJ10-3-37HB pumping unit under the given conditions is where the crank angle is 178°7'3" and 358°2'37".This method is available in both pre-balanced pumping unit and the one whose crank can rotate in all directions,and it is reference to research other styles pumping units.