A semiconductor module comprises a mounting board. A plurality of power switching device chips are mounted on the mounting board by flip-chip bonding. The chip has an upper surface and a lower surface and is configured to face the upper surface toward the mounting board. A drive IC chip is mounted on the mounting board by flip-chip bonding. The drive IC chip is operative to drive gates of transistors formed in the plurality of power switching device chips. A plurality of heat sink members are located on the lower surfaces of the plurality of power switching device chips, respectively. A resinous member is provided to seal the plurality of power switching device chips and the drive IC chip in a single package.