The results of dc and ac magnetization, heat-capacity, 57Fe Moessbauer spectroscopy, dielectric, pyroelectric current and isothermal magneto-capacitance measurements on a recently reported lithium-based oxide, Li3FeRuO6, related to LiCoO2-type rhombohedral structure (space group, R-3m) are presented. The results reveal that the compound undergoes spin-glass freezing below 15 K. There is a peak around 34 K in pyroelectric data, which can not be attributed to ferroelectricity, but to the phenomenon of thermally stimulated depolarization current. As revealed by magnetocapacitance data above and below magnetic ordering temperature, magnetic and electric dipoles appear to be coupled, thereby offering evidence for magnetodielectric coupling.