A cylinder head cooling structure is provided with: an intake-side cooling flow passage 20; inter-cylinder cooling flow passages 23; inter-port cooling flow passages 24; first cooling water supply flow passages 25A to 25C having upstream ends which are connected to a cooling water supply passage 50 provided in a cylinder block 2 of an engine, and downstream ends which merge with the upstream endsof the inter-cylinder cooling flow passages 23; and isolating walls 30 which are provided extending obliquely within the inter-cylinder cooling flow passages 23, from upstream side cylinder exhaust ports 12B to exhaust side cylinder intake ports 13A, thereby dividing the inter-cylinder cooling flow passages 23.