An electro-hydraulic variable valve lift apparatus may include a housing, a master portion which is slidably disposed to the housing and contacts a cam, a first oil supply portion which supplies hydraulic pressure, a slave piston which is slidably disposed within the housing and defines an oil chamber with the master portion, a latching portion which is supplied the hydraulic pressure from the first oil supply portion and selectively connects the slave piston and the master portion, a second oil supply portion which selectively supplies hydraulic pressure to the oil chamber so as to control relative distances between the master portion and the slave piston when the slave piston is disengaged with the master portion, and a stepped portion formed to the housing between the master portion and the slave piston to elastically support the master portion.