The continuous zoom function is one of the important features of the current advanced thermal imaging cameras, and the zoom cam is the key component to drive the movement of each lens group in the continuous zoom optical system. First, this study applies the dynamic optics theory to deduce the image movement compensation group formula of the zoom optical system to obtain the trajectory curve of the image movement compensation group and design a zoom cam structure with good performance. Then, we use the sequential quadratic programming (SQP) optimization algorithm. Combined with the optomechanical design theory, CREO is used to generate the cam curve and cut the cam groove to obtain the zoom cam structure and reduce the pressure angle of the dynamic optical curve. Then, the cam structure is analyzed based on the finite element analysis theory. Finally, the motion of the zoom system and the imaging results confirm the feasibility of the proposed method.