A composite core panel has opposite side surfaces for receiving skins to form a composite sandwich panel. The core panel includes a plurality of spaced blocks of low density cellular material such as foam plastics and have opposite side surfaces forming the side surfaces of the core panel and opposite edge surfaces extending between the side surfaces. A plurality of parallel spaced elongated primary strips of structural cellular material such as balsa wood or engineered foam have a higher density and extend between the blocks, and the blocks have side surfaces adhesively attached to edge surfaces of the blocks. A plurality of parallel spaced secondary strips of structural high density cellular material such as balsa wood or engineered foam extend transversely to the primary strips and have end surfaces adhesively attached to the primary strips and side surfaces adhesively attached to the blocks.