We fabricate a long-period grating band-rejection filter with a lithium niobate $\left({\text{LiNbO}}_3\right)$ channel waveguide, where the grating is formed on the waveguide surface by plasma reactive ion etching. The filter shows three distinct thermal tuning regimes. Below $\sim 55°\text{C}$ , the center wavelength of the rejection band decreases linearly with an increase in the temperature at a high sensitivity $\left(-1.4\text{\hspace{0.17em} nm}/°\text{C}\right)$ . The temperature sensitivity drops abruptly to a negligible value at $\sim 55°\text{C}$ and stays low up to $\sim 70°\text{C}$ , above which it jumps abruptly to a large positive value $\left(1.6\text{\hspace{0.17em} nm}/°\text{C}\right)$ . We attribute these peculiar tuning characteristics to the formation of different crystal phases in the core and cladding areas of the ${\text{LiNbO}}_3$ waveguide and the abrupt transitions of the thermo-optic coefficients of some crystal phases. The grating could be developed into various kinds of integrated-optic filters and switches for application in optical signal processing.