ABSTRACT: Vibrational analysis of beams has been an important subject for many years. Despite the wide applications of curved beams, especially laminated composite curved beams, less attention has been paid to this subject. In this study, the transient response of the laminated composite curved beam due to a moving force with constant velocity for different boundary conditions has been obtained. By employing Hamilton’s principle, the equations of motion along with the corresponding boundary conditions of the beam are determined. The finite element method is employed to solve these equations. Using the eigenvalue technique, the vibrational characteristics of the beam are calculated. Results for the free and forced vibration of the beam have been compared against available data in the literature and the three-dimensional model in ANSYS. The effects of different parameters such as the geometry of the beam, fibers orientation, and boundary conditions on the transient response of the beam have been investigated. It has been shown that beam with cross-ply layups has lower values of transient deflection compared to the angle-ply layups. Also, the anti-symmetric cross-ply beam has more deflection with respect to the symmetric one.