The existing displacement of parallel + serial type hybrid mechanisms is mainly solved by the equivalent serial mechanism (SM) method. However, a large number of lower mobility parallel mechanisms (PMs) that have high coupled motions at the end-effector cannot be equivalent to SMs. Thus, the displacement problem especially for the inverse displacement of this type of hybrid mechanisms has not been well solved. On the basis of this situation, this article takes a 6-degrees-of-freedom (DOFs) 3-UPU + 3R hybrid mechanism as an example to give a general method to solve the displacement problem. First, based on the inverse displacement and pose coupling relationship of the 3-UPU PM, its forward displacement is solved by Sylvester’s dialytic elimination method, and then the forward displacement of the 3-UPU + 3R hybrid mechanism is obtained by the superposition method. Second, by skillfully dealing with the relationship between coupling motions of the 3-UPU PM and the motion of hybrid mechanism, three nonlinear equations containing three unknown motion parameters are obtained, and the inverse displacement problem is solved using Sylvester’s dialytic elimination. The research in this article is valuable in the kinematics modeling of hybrid mechanisms.