There are provided a highly thermal conductive grease composition having both a thermal conductivity and a satisfactory dispense property, and a cooling device applied with same. The grease composition comprises from 70 to 90% by volume of an inorganic powder which is a mixture containing at least two kinds of inorganic powders different from each other in each average particle size, and from 10 to 30% by volume of a base oil containing a mineral oil or a synthetic oil, the base oil further containing a surfactant in an amount of from 0.2 to 2.0% by weight based on the weight of the inorganic powder.