An omni-directional stereo system has a wider field-of-view than conventional cameras, and is widely used in many applications such as robots navigation, depth estimation, and 3D reconstruction. Existing approaches usually use single viewpoint (SVP) systems as the imaging sensor. However, literature proves that an efficient SVP of an omni-directional system can only be achieved with precisely aligned mirrors of parabolic or hyperbolic profile. This enforces rigorous restriction on the configuration of camera and mirrors. In fact, some other profiles, though they do not have the SVP property, are desirable for certain reasons such as cheaper cost and more practical implementation. Therefore, in this paper, we propose both a typical nonsingle viewpoint (non-SVP) omni-directional stereo sensor and its corresponding depth estimation method based on graph-cuts optimization. The sensor comprises a perspective camera and two separate reflective mirrors that could be any radially-symmetric ones. To formulate the depth estimation more consistent with the proposed sensor, we divide the depth space of scenes with a sequence of virtual coaxial cylindrical layers, and model depth estimation as a labeling problem. In the labeling procedure, by considering the characteristics of an omni-directional image, we further devise novel tangential-neighborhood system, radial-neighborhood system, and depth-gradual-changing smoothness constraint which perform better than traditional ones. Depth estimation and 3D reconstruction for both synthesis and real scenes justify the effectiveness of the proposed method.