Along the beam lines of the SuperKEKB main rings, 218 conventional sextupole magnets are installed, and they are used for tuning the chromaticity of the accelerator rings. Especially, 16 sextupole magnets in the beam straight lines in the Tsukuba area are quite essential for the Crab Waist beam colliding. To make the beam tuning process finer, we are studying the superconducting sextupole magnet system with three types of the corrector magnets. From the operation temperature of the system, A15 compound superconductor is chosen as the cable material, and the development of the react and wind coil production has been tried with the Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Al cable. The Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Al super fine strand superconducting cable for the corrector magnets was manufactured, and its superconducting characteristics are being studied. In this paper, as the first test result of the development, the critical current characteristics of the straight cable as variables of temperature and magnetic field are reported. As the results, the critical current of the Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Al cable was higher than the design values for the corrector magnets, and this level of cable performance also indicates the potential for the cable being used for the main sextupole magnet.