This paper first presents an analytical model for a new kind of braided composite called 3D surface-core 4-directional braided composite. Taking into account the braiding process, three types of microstructural unit-cell models are established with respect to the interior, surface, and corner regions. According to the spatial paths and squeezing deformation of yarns in the material, different braiding angles and cross-section shapes are adopted. By using the volume averaging method, the total stiffness is calculated and the engineering elastic constants are obtained. The effect of braiding angle and fiber volume fraction on the stiffness is addressed. The theoretical predictions are in good agreement with the experimental data. The effects of edge cuttings on the longitudinal tensile properties of the new material and 3D 4-directional braided composites are experimentally compared. The proposed structure has obvious advantage to restrain the degradation of mechanical properties caused by cuttings.