A theoretical study of a cylindrical anisotropic optical fiber filled inhomogeneously by an anisotropic metamaterial is carried out. Nanoporous alumina microtubes obtained recently by acid anodization techniques are physical manifestations of such optical waveguides. In these microtubes, the nanopores are aligned radially outward and the nanopore diameters vary radially, rendering the system inhomogeneous. By considering the radial variation of the nanopore size, a local permittivity tensor is obtained by a Maxwell-Garnett homogenization theory. The cylindrically anisotropic and inhomogeneously filled fiber is shown to support propagating modes of hybrid polarization character (EH or HE modes). The salient feature of this system is that the modal fields are extremely confined near the center of the waveguide due to the refractive inhomogeneity. The anisotropy plays a relatively minor role in the localization. The easy control over the dielectric anisotropy and the inhomogeneity made possible in the nanoporous alumina fiber makes it an attractive candidate for nanophotonic applications.