We report the surface structure and roughness of the mirrors made of carbon fiber reinforced silicon carbide (C/SiC) composite improved for the SPICA (Space Infrared telescope for Cosmology and Astrophysics) mission. The improved C/SiC is a candidate of material for the SPICA light weight mirrors because of its superior properties: high toughness, high stiffness, small thermal deformation, feasibility to make large single dish mirror, low cost, and short term for production. The surface of the bare C/SiC composite consists of carbon fiber, silicon carbide and silicon, each of which has different hardness, so it is difficult to polish this surface smoothly. Our improved polishing technique achieved the surface roughness of better than 20nm RMS for the C/SiC composite flat mirror, which satisfies the requirement of the SPICA mission. For curved bare surface of the C/SiC mirror, the roughness is larger than 30 nm and now under improving. The Change of Bidirectional reflectance distribution function (BRDF) of the bare C/SiC composite at cryogenic temperature was measured with 632.8nm lasar. No significant difference was found between the BRDFs at 95K and that at room temperature. In order to improve surface roughness further, we are planning to apply the SiSiC slurry coating on the surface of the improved C/SiC composite. This combination can realize the surface roughness well enough to be applied even for optical telescopes.