Abstract: To adapt to the high speed of modern rapier looms and the requirement of rapier motion curve,a new design method of transitional curve of modified trapezoid acceleration motion for rapier is put forward,which uses high order polynomial as transitional curve.The method takes into account not only boundary condition but also midpoint and 1/4 node,so the two joints of transitional curve are of slick transition.In this way,the rapier motions placidly and rapidly.It has more advantages and is fit for high speed looms.