This study proposes a large-scale modular deployable mechanical network constructed by networking Altmann linkages, which are spatial single-loop mechanisms with six revolute joints and four bars, and develops a theoretical approach to verify the feasibility of the networking method. First, the screw motion equation of the linkage is derived, and the deployability of the linkage is demonstrated through a motion simulation. Second, using the overlapping-unit method, a deployable mechanical network is constructed. The constraint graph of the mechanical network is deduced subsequently. The mobility of the mechanical network is proved by screw theory, which demonstrates the feasibility of the networking method. Then, the motion of the mechanical network is simulated and it is found to have excellent deployability. Finally, a prototype of the mechanical network is fabricated. Results show that spatial single-loop linkages can construct modular deployable mechanical networks with the overlapping-unit method under appropriate connections. This networking method can be verified with the theoretical approach proposed in this work.