The complex dielectric constant, epsilon = epsilon' + i-epsilon", of ice at 26.5-40 GHz was determined using free-space measurement technique. A network analyzer-based system was used to measure the phase velocity and attenuation of a synthesized pulse propagating in bubble-free ice which was grown from distilled de-ionized water. Based on the phase velocity measurement, epsilon' was determined to be 3.155 +/- 0.005 and virtually independent of frequency. The loss factor in ice was observed to be frequency dependent so that epsilon" increased from approximately 0.002 at the lower frequencies to 0.004 at the higher frequencies. No temperature dependence of epsilon' and epsilon" was observed at ice temperatures of - 2.5 and - 15-degrees-C.