A hood hinge apparatus for a vehicle, in which a cowl-side body connected with an A-pillar has an inclined structure or an angular structure having a larger inclination than a right angle to reduce a step between the A-pillar and the cowl-side body, and engagement bolts are engaged with a horizontal inclined surface and a vertical inclined surface in different directions for coupling between the cowl-side body and the fixed hinge bracket to prevent injury of a passenger due to excessive dipping caused by generation of body bending during a front offset collision, thereby actively responding to safety regulations in case of a collision.