It is very important for bogie design process to calculate the parameter expression of coupling displacement ability required by a bogie and the affect of each parameter on the required displacement ability, which will make the designer to grasp the design initiative and make the design more efficient. The parameter expression of coupling displacement ability required by a bogie was obtained which was applicable for bogie with motor suspended on frame and gear box suspended by a suspender. For similar bogies, it was simple to obtain the required coupling displacement ability and the curves changing with relevant parameter by entering the values of the parameters to improve the design finally. Firstly, the geometrical model based on the actual structure was proposed, and then equations were obtained by using analytical method and solved gradually with Matlab. At last, the parameter expression of required coupling displacement ability was obtained which was proved right by substitution and Pro/ENGINEER method. For a specific bogie dimension, the curves of required displacement ability changing with relevant parameters were drawn and the results showed that horizontal distance between large gear axis and small gear axis, upper/lower end of suspender and large gear axis have a large effect on the required coupling displacement ability.