Superconducting planar terahertz (THz) metamaterials (MMs), with unit cells of different sizes, are fabricated on 200 nm-thick niobium nitride (NbN) films deposited on MgO substrates. They are characterized using THz time domain spectroscopy over a temperature range from 8.1 K to 300 K, crossing the critical temperature of NbN films. As the gap frequency (f(g) = 2Δ0/h, where Δ0 is the energy gap at 0 K and h is the Plank constant) of NbN is 1.18 THz, the experimentally observed THz spectra span a frequency range from below f(g) to above it. We have found that, as the resonance frequency approaches f(g), the relative tuning range of MMs is quite wide (30%). We attribute this observation to the large change of kinetic inductance of superconducting film.