The stability of reticulated shell is a key issue for single-layer reticulated shell. In the paper, a single-layer arch-supported shell structure was analyzed by finite element software MIDAS. The eigenvalue buckling analysis and the geometric nonlinear overall stability analysis with initial imperfection of the model which carried two different load combinations were studied too. At the same time, the influences on the stability of the shell structure were researched. The results showed that the shell structure was sensitive to the initial imperfection. Under different load combinations, the instability of modes and limited capacity of stability are different in the shell structure.