Recent coded aperture imaging systems have shown great success in scene reconstruction, extended depth-of-field and light field imaging. By far nearly all solutions are built on top of commodity cameras equipped with a single spherical lens. In this paper, we explore coded aperture solutions on a special non-centric lens called the crossed-slit (XSlit) lens. An XSlit lens uses a relay of two orthogonal cylindrical lenses, each coupled with a slit-shaped aperture. Through ray geometry analysis, we first show that the XSlit lens produces a different and potentially advantageous depth-of-field than the regular spherical lens. We then present a coded aperture strategy that individually encodes each slit aperture, one with broadband code and the other with high depth discrepancy code, for scene recovery. Synthetic and real experiments validate our theory and demonstrate the advantages of XSlit coded aperture solutions over the spherical lens ones.