This paper is presented to improve the modeling accuracy and the computational stability for a high-speed rotating flexible structure. The differential governing equations are derived based on the first-order approximation coupling (FOAC) model theory in the framework of the generalized Hamiltonian principle. The semi-discrete model is obtained by the finite element method, and a new shape function based on FOAC is established for the piezoelectric layers. To increase the efficiency, accuracy, and stability of computation, first, the second-order half-implicit symplectic Runge–Kutta method is presented to keep the computational stability of the numerical simulation in a long period of time. Then, the idea of a precise integration method is introduced into the symplectic geometric algorithm. An improved symplectic precise integration method is developed to increase accuracy and efficiency. Several numerical examples are adopted to show the promise of the modeling and the computational method.