There are many types of pitching balls in baseball. The difference among types of pitching is caused by baseball’s “moving speed, rotating speed and axis of rotation”. It has been understood that the stitch of the ball is very important. These parameters change the fluid force acting on a baseball, and it causes different trajectories of the ball. In this study, we calculated flows around rotating and moving baseballs by using Cumulant-LBM. First, we analyze the flow around a sphere in high Reynolds number region and reproduce the drug crisis. Next, we study trajectories of a ball under various conditions by calculating the flow around the baseball.