Real and imaginary parts, epsilon' and epsilon", of the dielectric constant of Li2B4O7 were measured at temperatures of 10-300 K and at frequencies of 30 Hz-1.8 GHz, using two kinds of the single crystals prepared for a surface acoustic wave (SAW) device and for a nonlinear optical (OPT) device. Commonly to the both crystals, two new features were found: Debye-type dielectric dispersion appears near 2 GHz at room temperature, and a broad dielectric maximum occurs at approximately 120 K. On the other hand, only on the OPT crystal, epsilon' along the c-axis shows a small cusp at 220 K, and both epsilon' and epsilon" show sharp peaks at 237 K. These anomalies occur mainly on increasing temperature, and the magnitudes strongly depend on samples. In addition, the epsilon" along the c-axis increases rapidly with increasing temperature above about 230 K due to ionic conduction of mobile Li-ions as reported previously, but it shows an obvious thermal hysteresis in the temperature range of 230-300 K. We discuss causes of these peculiar dielectric behaviors above 220K, by assuming an interaction between an incommensurate modulation wave and Li-ions, which are mobile at room temperature and freeze at low temperatures below about 230 K.