An apparatus for opening and closing an engine hood for a construction machine is disclosed that can open an engine hood at an angle desired by an operator. The apparatus for opening and closing an engine hood includes a frame having one side fixed to an upper swing structure and the other side fixed to a cowl frame, a guide rail having a guide groove formed in a length direction and a plurality of seat portions formed to be cut so as to communicate in a downward direction with respect to the guide groove and maintaining an opening angle that is set to open the engine hood in multiple stages, and a stay rod having a free end slidably formed along the guide rail and a fixed end rotatably fixed to the engine hood.