Optical polarization anisotropy of single crystals of AlPO4-5 (AFI) containing carbon nanotubes is studied to develop the optical characterization method of the samples by laser micro-polarimetry at 488 nm. The crystals are opaque in the configuration, KC with EC, but are almost transparent in the configuration, KC with E||C, where K and E are the wave vector and the electric field of the incident light, respectively. The degree of polarization reaches almost unity at the maximum. When K||C, they are also transparent for any directions of E except for some locations including the surface. The strong luminescence bands are observed at 540 nm and 570 nm with the tail toward long wavelength region. The 3D imaging of the luminescence is performed by Nanofinder to demonstrate their extrinsic origin.