This paper establishes the parameters of the ball trajectory based on the fractional differential equation model. At the same time, this paper quantifies the shooting power of direct free kicks. In this paper, the resistance effect of air on the motion of the center of mass is considered. And the dynamic equation of the football arc motion is established. In this way, we obtain the analytical solution of the differential equation of order. The research shows that the correlation between the fitting equation of the football flight trajectory and the prediction equation is 96.55%. The algorithm model in this paper can effectively predict the flight path of football. The research theory of this paper provides a theoretical basis for football offensive training strategies.