An apparatus for controlling turbine blade tip clearance comprising: a turbine casing configured to guide a flow of combustion gas; an actuator ring rotatably mounted outside the turbine casing; a plurality of turbine blades rotatably mounted inside the turbine casing; a plurality of ring segments surrounding tips of the turbine blades and installed to form a predetermined gap with each tip; a plurality of rotary shafts each configured to have one end connected to several of the plurality of ring segments and the other end extending radially from the turbine casing; a link member configured to rotate an associated one of the rotary shafts according to circumferential rotational motion of the actuator ring; a pusher member provided at an inner end of the rotary shaft to move the several ring segments radially inward by rotation of the rotary shaft, characterized in that the apparatus further comprises, a bearing bracket mounted outside the plurality of ring segments and installed such that the pusher member passes through the bearing bracket; a screw bush mounted in a center of the bearing bracket such that the pusher member passes through the screw bush and configured to move the pusher member radially when the pusher member rotates; and a pair of elastic restoration devices mounted between both sides of the bearing bracket and the ring segments and configured to restore force during contraction to pull the ring segments radially outward to maintain the gap above a predetermined value, wherein each of the elastic restoration devices comprises a mounting shaft having one end coupled to an associated one of the ring segments and the other end coupled to the bearing bracket, a spring mounting member fixed to the bearing bracket by a coupling member and having a through-hole through which the mounting shaft passes, and a spring having one end coupled to the ring segment and the other end coupled to the spring mounting member, the spring being disposed around the mounting shaft. a turbine casing configured to guide a flow of combustion gas; an actuator ring rotatably mounted outside the turbine casing; a plurality of turbine blades rotatably mounted inside the turbine casing; a plurality of ring segments surrounding tips of the turbine blades and installed to form a predetermined gap with each tip; a plurality of rotary shafts each configured to have one end connected to several of the plurality of ring segments and the other end extending radially from the turbine casing; a link member configured to rotate an associated one of the rotary shafts according to circumferential rotational motion of the actuator ring; a pusher member provided at an inner end of the rotary shaft to move the several ring segments radially inward by rotation of the rotary shaft, characterized in that the apparatus further comprises, a bearing bracket mounted outside the plurality of ring segments and installed such that the pusher member passes through the bearing bracket; a screw bush mounted in a center of the bearing bracket such that the pusher member passes through the screw bush and configured to move the pusher member radially when the pusher member rotates; and a pair of elastic restoration devices mounted between both sides of the bearing bracket and the ring segments and configured to restore force during contraction to pull the ring segments radially outward to maintain the gap above a predetermined value, wherein each of the elastic restoration devices comprises a mounting shaft having one end coupled to an associated one of the ring segments and the other end coupled to the bearing bracket, a spring mounting member fixed to the bearing bracket by a coupling member and having a through-hole through which the mounting shaft passes, and a spring having one end coupled to the ring segment and the other end coupled to the spring mounting member, the spring being disposed around the mounting shaft.