Dielectric properties, ac conductivity and thermal characteristics of terbium fumarate heptahydrate crystals grown by gel diffusion method have been carried out. The real part of dielectric constant, dielectric loss and ac conductivity of the material have been measured as a function of temperature and frequency of the applied electric field. Dielectric constant, dielectric loss and ac conductivity of the title compound were systematically investigated, showing a hump at about 85 degrees C, which could be attributed to water molecules in the crystal boundary. The dielectric anomaly exhibited by the material has been correlated with its thermal behaviour. The ac conductivity of the material obeys the Jonscher's power law relation; sigma(omega) = sigma(o) + A omega(s), with the temperature dependent power exponent s < 1. The ac conductivity of the compound has been found to increase with the increase in frequency. The material is suggested to show protonic conduction. The non- isothermal kinetics was used to evaluate the activation energy for the dehydration step of thermal decomposition of terbium fumarate heptahydrate by using the Coats -Redfern integral method. (C) 2014 Elsevier B. V. All rights reserved.