Superconducting critical temperature, T-c, and the shielding volume fraction, SVF, of layered nitride superconductor NaxHfNCl have been studied as a function of x, i.e. Na concentration. Although T-c decreases gradually with increasing x from 20.0 K at x = 0.11 to 16.5 K at x = 0.85, SVF has a sharp peak around x = 1/6, where strong coupling between local ordering of Na atoms and Fermi surface instability can be expected. Structural disorder in the samples above x = 0.5, observed by powder neutron diffraction, does nor affect the superconductivity appreciably. Electronic specific heat coefficient, gamma, is estimated to be about 7.7 mJ/mol/K-2 by its difference of magnetic susceptibility between HfNCl and Na0.5HfNCl. The gamma value is relatively small compared with the high T-c value, revealing double honeycomb lattice system as new potential higher T-c superconductor series by intercalation.