Abstract: The global stability of vaneless diffuser in the centrifugal compressor is often influenced by the main flow stability, backflow at exit and the boundary layer separation. For the vaneless diffuser with large axial width ratio, the effect of the main flow and boundary layer on the instability perturbations is the main subject. In this paper, the mean flow of the wide vaneless diffuser is firstly obtained with numerical simulations. The Eulers' and Navier-Stokes equations are linearized respectively based on the small perturbations assumption. Then the inviscid stability approach considering the inviscid main flow and the mixed stability approach considering the effect of both eddy viscosity and molecular viscosity are established. The prediction results are validated against the experimental results. At last, the structural sensitivity based on the adjoint method is adopted. And the wave-maker region is revealed under different treatments of viscosity. The instability perturbations are located at the middle of the flow field when inviscid main flow is only considered. And a centrifugal instability maybe the main cause of the vaneless diffuser stall. When the inviscid main flow and boundary layer are both considered, the wave-maker region not only lies at the main flow near the middle of the vaneless diffuser, but also lies at the reverse flow region of the boundary layer.