We consider the stabilization of star-shaped network with moving boundary. The network consists of a single node with 3 connected arcs. The dynamics on each arc is governed by the wave equation. There is boundary damping at the first two boundary points. At the central node, the states are coupled by algebraic conditions. We show the solution behaviour of star-shaped network with Neumann boundary conditions, that is, the energy of star-shaped network with mixed boundary conditions decrease or not depending on the different range of parameter.