An electric drive motorcycle (100) allows a suitable and effective cooling of the battery unit when the electric motor is operated, and comprises: a front portion comprising one or more front wheels (103) and a handlebar (104); a rear portion comprising a saddle (101), a shell body (107) arranged below said saddle (101), and a rear wheel (105) arranged below said shell body (107); an intermediate portion extending as a connection between said front portion and said rear portion; an electric drive unit (8) connected to said rear wheel (105); and a hybrid supply unit supplying said electric drive unit (8), comprising at least a battery unit (115) and a combustion engine (116) actuating an electric generator (120) apt to feed said battery unit (115) and/or said electric drive unit (8), wherein the combustion engine (116) drives a cooling fan (121) arranged so that, when this is drawing a flow of cooling air through an inlet mouth (122), such flow wets the battery unit (115), before being drawn, wherein the combustion engine (116) comprises a crankshaft which is arranged transversally to said front-rear direction, said crankshaft having a first end keyed to an electric generator (120) arranged adjacent to the wall of the shell body (107), and a second end thereto said cooling fan (121) is keyed, and wherein the sucking mouth (122) of the cooling fan (121) is faced towards the battery unit (115).