We studied the polymerization of ethylene monomers with chromocene catalyst to produce polyethylene with low dielectric loss in the microwave region. Chromocene (bis-cyclopentadienyl chromium) is very active for a long period during ethylene polymerization, and it also has a very low dipole moment because of its symmetrical molecular structure. Polyethylene polymerized by using chromocene has a low dielectric loss in the 500 MHz region caused by gamma relaxation. We were able to calculate the loss in this wavelength region from a summation of each individual contribution. The contributors included catalyst residue, and polar groups, i.e., methyl groups and double bonds such as vinyl, internal trans-vinylene, and vinylidene groups at a certain crystallinity. In order to make low dielectric loss polyethylene with a chromocene catalyst, we first tried to improve both the process of ethylene polymerization with a chromocene catalyst and the dielectric loss (tan delta) of polyethylene at 500 MHz. We measured the number of polar groups and the residual catalyst in polyethylene with the IR method. Our results revealed that both the hydrogenation reaction that occurs during ethylene polymerization with the chromocene catalyst and the crystallization of polyethylene after polymerization were very effective in reducing the dielectric loss of polyethylene.