A design method of beam-converting annular resonator is presented. And the bare cavity modes of this resonator are calculated, the advantages of beam-converting annular resonator are analysed. The cavity′s stability is also studied with home-made three-dimensional ray tracking program. It showed that beam-converting aannular resonator is a valuable resonator with high extraction effiecency and near-diffractive-limit optical quality, and can sustain certain disturbance. The methods presented are also valuable to the design and calculation of other complex laser resonators.