In our previous research, it was demonstrated that the moving bed air reactor in a chemical looping combustion system has advantages of stable solid flow, low pressure drops and flexible adjustment. However, the presence of stagnant zone in the reactor affects efficient heat and mass transfer and causes sintering and agglomeration of the oxygen carrier. Thus, it is of vital importance to understand the properties of dense granular flow in the moving bed. The investigations on the macroscopic phenomena such as the flow pattern, solid residence time, solid flow rate, etc. have been extensively conducted before in our previous research, but the focus on interparticle contact force network which dominates the macroscopic phenomena has been lacking. To evaluate the movements of solids at mesoscale and mitigate the stagnant zone in the moving bed air reactor, the discrete element simulations are conducted, and force chain structure properties are extracted from the complex network. Results show that the network of inter-particle contact force is denser than the force chain network. Most of the force chain consists of 3-6 particles, and the number of force chain decreases with increase in length of force chain. In addition, the force chain structure and evolution characteristics of various types of internals are discussed in detail, and the effects of arrangement of internals are evaluated. The in-depth analysis of spatiotemporal evolution features of force chain structure provides new insights in understanding of the stagnant zone in moving bed air reactor and is very beneficial for reactor optimization.