A stucco construction system and method of installing the stucco construction system that includes a substrate, a first sheathing, a plurality of brackets, a plurality of insulation panels, a second sheathing and a stucco layer. The substrate has a first side and a second side. The first sheathing extends over the second side of the substrate. The plurality of brackets is positioned on the second side of the first sheathing and are coupled to one of the substrate and the first sheathing. The plurality of brackets are spaced apart from each other. The plurality of insulation panels is positioned such that each insulation panel is positioned between the plurality of brackets. The second sheathing extends over the plurality of brackets and the insulation panels and is attached to the plurality of brackets. The stucco layer is disposed over the second sheathing.