This paper investigates the dynamic response of space flexible structures with control moment gyroscopics (CMGs) in which uncertain-but-bounded parameters are considered. The uncertainties in the dynamic modeling of flexible structure are treated as interval parameters and an interval gyroscopic model is established. Afterwards, a rational series expansion-interval perturbation finite element method (RSE-IPFEM) is proposed to estimate the upper and lower bounds of the interval dynamic response of the gyroscopic flexible structure. Meanwhile, the Monte Carlo method is presented to provide a reference solution. Two numerical cases are given to demonstrate the effectiveness and feasibility of the RSE-IPFEM. The results show that the uncertainties of Young’s modulus and rotor speed have a great impact on the dynamic response of the gyroscopic flexible structure.