Door handle structure of vehicle

A lever is configured to be rotatable around a rotational support axis among a storage position where the lever is flush with a door outer panel, a gripping position where the lever is projected from the door outer panel by driving of a driving unit so that a user is able to grip the lever, and an open position where the lever is further projected from said gripping position. The driving unit is fixed in an opposite area of a hinge arm which is opposite, relative to the rotational support axis, to an area of the hinge arm where the lever is arranged. The above-described area of the hinge arm where the lever is arranged and the driving unit are provided to face each other relative to the rotational support axis when the lever takes the storage position.