An electronic device enclosure assembly with a connecting assembly is disclosed. The electronic device enclosure assembly includes two electronic device enclosures. Each of the two electronic device enclosures includes a top frame, a bottom frame, a plurality of supports and a maintaining pole. The plurality of supports connects the top frame and the bottom frame, the maintaining pole is secured between two of the plurality of supports, and the maintaining pole defines a securing slot. A mounting member includes two side plates opposite to each other, and a positioning member protrudes from each of the two side plates. The maintaining poles of the two electronic device enclosures are located between the two side plates, the positioning member is engaged in the securing slot, and the two electronic device enclosures are connected together by the mounting member.