Surface accuracy is one of the most crucial indicators for evaluating the performance of a large deployable antenna. It depends on the accuracy of the truss structure of the truss antenna. This paper presents a novel method for accurate analysis of a large deployable truss antenna with 3D joint clearances. The proposed method does not depend on the structure’s style, which is suitable for general multi-closed-loop structures. Firstly, the clearance model of the truss structure is established using a vector description. Then, an error transfer path analysis method is proposed for the multi-closed-loop structure. The distribution probability of the truss antenna’s surface accuracy is also obtained. The efficiency of the method is validated through a numerical example of a planar mechanism with a multi-closed loop. The proposed method is also applied to analyze the surface accuracy of the large deployable antenna with a parabolic cylindrical truss.