To simulate the mass separation or mixture for chemical or biological fluids with viscoelastic characteristics, the rotating electroosmotic flow (EOF) of two-layer fluid in a microchannel with parallel plates is studied. This system is composed of Newtonian fluid and Caputo fractional Oldroyd-B fluid. Maxwell stress is introduced to describe the interaction of two fluids at the interface as well as the shear stress. Based on L1 approximation, numerical solutions are obtained by the finite difference method. The results show that mainstream velocity will oscillate first and then reach a stable state as there is enough time. Due to the existence of centrifugal force, mainstream velocity will increase with the increasing rotating angular velocity. Furthermore, the minimum value of velocity does not lie at the middle of channel because of viscoelastic effects, and the position where reverse flow appears also is pushed to the right side of the center when the rotating angular velocity is large enough. Moreover, with the increase of the interfacial zeta potential difference, the velocity distributions of two-layer fluid have different trends.