The vibration analysis of curved composite structures under the moving vehicles, is rarely investigated in litreture. Therefore, this paper is studied the dynamic response of a simply supported laminated deep curved beam under a moving load based on Timoshenko beam theory.It is assumed that the curvature of the beam and the amplitude and the speed of the moving load areconstant.The governing equations of motion for the system is extracted by Hamilton principles. A numerical and analytical methods are applied to obtain the dynamic response of the system.Also, the critical speed of the moving load and the fundamental frequency of the beam are obtained. The effects of the moving load characteristics, geometrical and material parameters such as the moving load speed, the radius of curvature and the modulus of elasticity in principal direction on the dynamic responses, fundamental frequency and critical speed of the system are investigated. The results show that the minimum and maximum deflection of the beam are occurred for lay-up [90/0/90/0] and [45/-45/-45/45]respectively. Furethermore, the increasing of the speed movingload leads to the decreasing thedynamic deflection. It is also shown that the increasing of the radius of the curved beams leads to the decreasingof the frequency and critical speed moving load.