PURPOSE: An apparatus for controlling position of strip in continuous annealing furnace is provided to prevent mistracking and heat buckle generated on the strip by controlling position of the strip considering tension applied to both ends of the strip. CONSTITUTION: In a strip position control apparatus comprising a string roll(2) rotated to move strip in a continuous annealing furnace, and a cylinder(3) for controlling upper and lower positions of the string roll by length of rod of the cylinder, the apparatus comprises a position detection part for detecting position of the strip by a region in which light projected from a light emitter(4) arrives at a light receiver(5) through the strip; a tension detection part(8) installed at left and right sides of the string roll to detect tension at both ends of the string roll; a control part(14) for converting the computed tension comparison value and the computed position comparison value into operation signals of the cylinder by computing the tension comparison value and position comparison value after comparing tension values of the tension detection part with a set tension value and comparing strip position values of the position detection part with a set strip center position value; a cylinder driving part(13) for controlling length of the cylinder rod according to output signals of the control part; and a string roll driving part for fixing the string roll in the annealing furnace and vertically driving the string roll as a connection means of the cylinder and the string roll.