In this work, we propose a multiband linear-polarization (LP) conversion and circular polarization (CP) maintaining reflector using a symmetric anisotropic metasurface. The anisotropic metasurface is composed of a square array of a two-corner-cut square multiring disk printed on a grounded dielectric substrate, which is a symmetric structure with a pair of mutually perpendicular symmetric axes u and v along the +/- 45 degrees directions with respect to the y-axis direction. The simulated results show that the reflector can realize LP conversion in five frequency bands at both x- and y-polarized incidence, the first four bands all have a certain bandwidth, and the fourth one, especially, is an ultrawideband. In addition, because of the symmetry of the reflector structure, the polarization state of a CP wave can be maintained after reflection, and the magnitude of the copolarized reflection coefficient at the CP incidence is just equal to that of the crosspolarized reflection coefficient at the x- and y-polarized incidence. We analyze the root cause of the multiband LP conversion and CP maintaining reflection, and carry out one experiment to verify the proposed reflector.