A three-dimensional compressible flow model is presented to study the occurrence of weak rotating waves in vaneless diffusers of centrifugal compressors. The diffuser considered has two parallel walls, and the undisturbed flow is assumed to be circumferentially uniform, isentropic, and to have no axial velocity. Linearized 3D compressible Euler equations were casted on a rotating coordinate system traveling at the same angular speed as the wave cells. A uniform static pressure at the outlet of the diffuser was imposed. Complex functions of the solutions to the equations were obtained by a second-order finite difference method and the singular value decomposition technique. The influences of the inlet Mach number of undisturbed flow, inlet spanwise distribution of undisturbed radial velocity, and diffuser radius ratio on the rotating waves were studied and results show that (1) the critical flow angle and rotating wave speed are both affected by the Mach number. However, the angle only increases slightly with the Mach number while the wave speed increases rapidly with the Mach number; (2) inlet distribution has minor influences on diffuser instability but the wave speed increases with the inlet distortion; (3) diffuser instability increases rapidly and the wave speed decreases quickly with the diffuser radius ratio; and (4) backward traveling rotating wave may occur if diffuser is sufficiently long and the inlet Mach number is sufficiently small.