In this paper, dynamic response of simply-supported composite sandwich beam with viscoelastic and transverse flexible core is investigated, analytically. Three-layered sandwich panel theory is used to analyze the beam. Hamilton's principle is employed to obtain governing equations of motion. In this paper, GHM method is used to model the viscoelastic core of the beam. Advantage of GHM model in according to classical models is including the frequency dependent characteristic of viscoelastic materials. Modal superposition method is used to convert partial differential equations of motion to ordinary differential equations with time varying coefficients. Newmark method is applied to solve the ODE with a numerical approach. Results of the present model are validated by analytical results published in the literatures. Innovation of this paper is considering frequency dependency of material property in viscoelastic core with using GHM model and utilizing three-layered sandwich panel theory in dynamic analysis of composite sandwich beam. The article investigates the dynamic response of beam with viscoelastic core by using GHM model to illustrate advantages of the GHM model over the Kelvin-Voigt model. As well as, a parametric study is also included in this paper to investigate the effect of different parameters such as thickness and density of core and stiffness of composite sandwich beam face sheets on the beam frequency and damping rate of beam dynamic response. The obtained results show that GHM model by considering the frequency dependency behavior of viscoelastic material presents a more accurate description of dynamic response of the beam with viscoelastic core.