The linear and nonlinear dielectric properties of composites based on KIO3 and nanocrystalline Acetobacter Xylinum cellulose have been studied. This cellulose is structured so that it has a large amount of nano-channels with parallel arrangement and with diameters of 50 – 100 nm and the lengths being thousand-fold. The behavior of the linear dielectric permittivity of the bulk KIO3 was found to have four anomalies at the temperatures corresponding to phase transitions. The temperature elevations of 20 and 24 K, respectively, for the IV → III and III → II structural transitions were revealed for the KIO3 in the pores of the nanocrystalline cellulose relative to corresponding transition temperatures in the bulk KIO3. Possible causes for the revealed temperature elevations were discussed.