This work aims to study the shape recovery of aramid fiber-reinforced shape-memory epoxy resin composite (SMERs). A circular tube can be assumed to be composed of a pair of curved tape with the same radius before being folded, and the middle position of this tubular structures is folded with a small curvature. The cylindrical shell is deformed into a flat shape at the folding line. So the shape memory fold-deploy experiments of the three deployable structures, flat tape, curved tape, and circular tube prepared with SMERs, were performed respectively, and the shape memory deployable processes were also simulated with finite element model. The temperature dependences of deployment angle, axial stress and axial strain in the shape memory folding step, cooling step, constraint removal step and reheating step were analyzed. The results showed that the full deployable process of each deployable structure was simulated well compared with experimental results. The strength failure in structure component occurred during the fold-deploy shape memory process. The long-term shear modulus of viscoelastic materials had a great influence on shape memory performance.