a mount apparatus of a vehicle having a structure for preventing separation of an insulator with a bracket , may include the bracket formed in a cylindrical pipe and covered with a rib at a side thereof , wherein the rib includes a hole , and the insulator coupled into the bracket , including , an inner core disposed in the bracket and an end portion thereof extending outside the hole of the rib , a first protrusion and a second protrusion formed to the inner core and extending toward the forward and rearward directions of the vehicle respectively in the bracket to prevent the insulator from separating from the bracket , wherein the first protrusion further protrudes than the second protrusion , and an insulating portion formed around the inner core .