Mobile networks, constructed with simple linkages by tessellation, have great application potential in engineering as they could change their shapes according to the need of working state by one degree-of-freedom (DOF). However, the existing one-DOF networks are always composed of bar-like links, and cooperated membranes should be designed and fabricated additionally, which makes the design and the realization more complicated. This paper is to construct a one-DOF network of Bennett linkages with identical square panels. Geometric conditions to construct the network are derived by investigating the kinematic compatibility, kinematics is carried out to show the relationships among all Bennett linkages, and the discussion on the design parameter shows the extensibility and the deploying performance, which is validated by two physical prototypes. This work initials the construction of mobile networks with identical polygon-like links, which will simplify the fabrication and realization of deployable structures.