A hinge apparatus of an engine hood for a vehicle which is provided between a hood panel and a vehicle body panel to ensure rotation of the hood panel. The hinge apparatus includes a hinge bracket mounted to a vehicle body panel, a hinge arm mounted to the hood panel and hinged to the hinge bracket by a hinge shaft and including a rail slot formed at one end thereof, a support link unit pivotally linking the hinge bracket to the hinge arm, and a return link unit pivotally linking the support link unit and the rail slot of the hinge arm so that the support link unit is selectively locked by the return link unit.