A valve opening duration control apparatus comprising: a camshaft; a cam unit on which a cam (71, 72) is formed, wherein the camshaft is inserted into the cam unit; a first guide bracket and a second guide bracket into which the camshaft is inserted; a wheel housing movably mounted to the first guide bracket and the second guide bracket, respectively; an internal wheel mounted on the camshaft and rotatably mounted on each wheel housing of the first guide bracket and the second guide bracket, wherein the internal wheel is configured of transmitting a rotation of the camshaft to the cam unit; a worm wheel mounted on the first guide bracket and the second guide bracket, respectively to engage with each wheel housing; a control shaft which is rotatably mounted on the first guide bracket and the second guide bracket, and engages with each worm wheel to move a position of the wheel housing according to rotation thereof; a connecting member that connects the first guide bracket and the second guide bracket; an upper guide boss formed on the first guide bracket and the second guide bracket, respectively; a guide shaft formed at the wheel housing, wherein the guide shaft is movably inserted into the upper guide boss and formed with a guide thread; an internal thread formed on an inside of the worm wheel and engaged with the guide thread, and an external thread formed on an outside of the worm wheel; and a control worm formed on the control shaft and engaging with the external thread, such that the worm wheel rotates by the rotation of the control shaft and changes the relative position of the wheel housing to the camshaft, such that, when the position of the wheel housing moves upper or lower relative to the rotation center portion of the camshaft, the relative rotation speed of the cams (71, 72) with respect to the rotation speed of the camshaft are changed. a camshaft; a cam unit on which a cam (71, 72) is formed, wherein the camshaft is inserted into the cam unit; a first guide bracket and a second guide bracket into which the camshaft is inserted; a wheel housing movably mounted to the first guide bracket and the second guide bracket, respectively; an internal wheel mounted on the camshaft and rotatably mounted on each wheel housing of the first guide bracket and the second guide bracket, wherein the internal wheel is configured of transmitting a rotation of the camshaft to the cam unit; a worm wheel mounted on the first guide bracket and the second guide bracket, respectively to engage with each wheel housing; a control shaft which is rotatably mounted on the first guide bracket and the second guide bracket, and engages with each worm wheel to move a position of the wheel housing according to rotation thereof; a connecting member that connects the first guide bracket and the second guide bracket; an upper guide boss formed on the first guide bracket and the second guide bracket, respectively; a guide shaft formed at the wheel housing, wherein the guide shaft is movably inserted into the upper guide boss and formed with a guide thread; an internal thread formed on an inside of the worm wheel and engaged with the guide thread, and an external thread formed on an outside of the worm wheel; and a control worm formed on the control shaft and engaging with the external thread, such that the worm wheel rotates by the rotation of the control shaft and changes the relative position of the wheel housing to the camshaft, such that, when the position of the wheel housing moves upper or lower relative to the rotation center portion of the camshaft, the relative rotation speed of the cams (71, 72) with respect to the rotation speed of the camshaft are changed.