This paper focuses on the fundamental vibration mode of the large deployable antenna structure. Here, the boundary conditions are considered as fixed Support according to the actual contact surface between the extended arm and truss. The grid mesh for the large deployable antenna structure is combined by both tetrahedral element and hexahedral element, where the hexahedral element is employed in the rod parts of the large deployable antenna structure, while tetrahedral element is in the joint parts of the large deployable antenna structure. The analysis results of the first four order models show that the four basic vibration forms of the antenna contain the twist motion, the bending motion, the roll motion and the breathing motion. These four vibration modes are important for the responses of the large deployable antenna, since they have the similar frequencies. It also analyzes the influence of material parameters and boundary conditions on the mode shape and frequencies. The results also provide the important reference to the selection of modal function and the nonlinear dynamic analysis of resonance parameters for the large deployable antenna. The study of the forced vibration through the harmonic response analysis is also meaningful to predict the dynamic behaviour and avoid resonance.