Prestress suspendome structure is a new two-double space structure system, which is composed of single-layer spherical reticulated shells and cable-strut tensile structure, and taking full advantages of two systems. Compared to single-layer shells, stiffness and stability are improved effectively. Compared to cable dome, designing, constructing and joint treatments are simplified much more easily. In this paper, taking geometrical nonlinearity and material nonlinearity into account, the stable ultimate bearing capacity of Schwedler suspendome was analyzed theoretically by employing a nonlinear finite element method. Structural parameters of the suspendome, such as prestresses of cables, heights of struts, rise-span ratio and cable layout, which influence the structural stable ultimate load-carrying capacity, having been analyzed by employing the two-double computational mode of Schwedler suspendome of 40m span. Some valuable and reasonable conclusions are drawn for practical engineering design by theoretically analysis.