A thermally conductive composition includes a matrix resin, a curing catalyst, and thermally conductive particles. The thermally conductive particles include, with respect to 100 parts by mass of the matrix resin component, (a) 900 parts by mass or more of aluminum nitride with an average particle size of 50 μm or more, (b) 400 parts by mass or more of aluminum nitride with an average particle size of 5 μm or less, and (c) more than 0 parts by mass and 400 parts by mass or less of alumina with an average particle size of 6 μm or less. A cured product of the thermally conductive composition has a thermal conductivity of 12 W/m·K or more and an Asker C hardness of 20 to 75. Thus, a thermally conductive composition having a hardness suitable for mounting to an electrical or electronic component and high thermal conductive properties, and a thermally conductive sheet using the thermally conductive composition are provided.