Layer-type oxide (NaxMx/2Ti1-x/2O2)-Ti-II-O-IV (M=Co, Ni; 0.60 less than or equal to x less than or equal to 1.0) has been prepared by solid state reactions. In both series, two structural variants of type alpha-NaFeO2 (O3) and beta-RbScO2 (P2) have been obtained consecutively as x decreases with a borderline composition around x(c) similar to 0.7. With the decrease of x, the ionic conductivity has been found to increase up to 8.4 x 10(-2) S cm(-1) at 770 K (Na0.67Co0.33Ti0.67O2). Compositions of P2 have been found to exhibit the conductivity values two to five times greater than those of O3, primarily due to the larger rectangular threshold available for the diffusion of Na+ ions. Such a structural effect has also been considered to depend on the polarizability of alkali ion. HT-XRD and Na-23-NMR data of Na0.67Co0.33Ti0.67O2 strongly suggest that the diffusion of Na+ ion is deeply related with the local distortion of trigonal prismatic sites, leading to the change of activation energy around 430 K.