A hinge supporting apparatus comprising: a connection member configured to hinge-connect a door to a main body; a cam member configured to vary an installation position of the connection member in order to control a gap between the main body and the door; and a fixing member configured to fix the connection member to the main body, wherein the connection member has an insertion hole which is formed thereon and into which the cam member is inserted, and the insertion hole includes a first end portion that corresponds to one side surface of the cam member and a second end portion which corresponds to the other side surface of the cam member that forms a pair with the one side surface of the cam member, wherein the cam member is set to have at least one posture with respect to the main body, and through the set posture, the cam member moves the connection member in any one of a first direction in which the connection member moves from the main body toward the door and a second direction in which the connection member moves opposite to the first direction, the hinge supporting apparatus being characterised in that the fixing member includes a bracket that is fixed to the main body and a pressing lever having one side that is rotatably connected to the bracket so as to clamp the connection member on the main body or to release clamping, and wherein the bracket includes a first and second portions (131, 132) which penetrate a first and second through-grooves (112a, 112b) formed at both side ends of the connection member and which hingeably support both ends of the lever, and a fixing portion into which a locking portion of the connecting member is inserted, and wherein the fixing portion allows the locking portion to be fixed in order to prevent it from moving in another direction than the first and second directions. a connection member configured to hinge-connect a door to a main body; a cam member configured to vary an installation position of the connection member in order to control a gap between the main body and the door; and a fixing member configured to fix the connection member to the main body, wherein the connection member has an insertion hole which is formed thereon and into which the cam member is inserted, and the insertion hole includes a first end portion that corresponds to one side surface of the cam member and a second end portion which corresponds to the other side surface of the cam member that forms a pair with the one side surface of the cam member, wherein the cam member is set to have at least one posture with respect to the main body, and through the set posture, the cam member moves the connection member in any one of a first direction in which the connection member moves from the main body toward the door and a second direction in which the connection member moves opposite to the first direction, the hinge supporting apparatus being characterised in that the fixing member includes a bracket that is fixed to the main body and a pressing lever having one side that is rotatably connected to the bracket so as to clamp the connection member on the main body or to release clamping, and wherein the bracket includes a first and second portions (131, 132) which penetrate a first and second through-grooves (112a, 112b) formed at both side ends of the connection member and which hingeably support both ends of the lever, and a fixing portion into which a locking portion of the connecting member is inserted, and wherein the fixing portion allows the locking portion to be fixed in order to prevent it from moving in another direction than the first and second directions.