To obtain the subject composite material with high mechanical strength, excellent in thermal conductivity, therefore suitable as a heat-radiative substrate or sliding part.

This composite material is such one as to be composed of Al or Si matrix and Si3N4 skeleton where columnar Si3N4 grains each ≥5 in mean aspect ratio (major axis/minor axis) are mutually and randomly bound in a three-dimensional manner through at least one rare earth element oxide binding phase, having a relative density of ≥98% and thermal conductivity of ≥130 W/mK.