Abstract: A combustor of a gas turbine having a double wall construction in one part of the combustor, wherein an outer plate is formed with a multiplicity of cooling air inlet apertures and an inner plate is formed with a multiplicity of cooling air outlet apertures. The inner and outer plates are connected together by a multiplicity of connectors formed of heat conductive material and define therebetween a space. The cooling air inlet apertures are greater in diameter but smaller in total area than the cooling air outlet apertures which are inclined at an angle of 30 degrees. Cooling air introduced into the space through the cooling air inlet apertures impinge on the inner surface of the inner plate and performs impinge cooling while the connectors perform pin fin cooling. The cooling air also performs film cooling as it flows along the outer surface of the inner plate after cooling the walls of the cooling air outlet apertures while being released.