This study proposes a closed-loop shaping control method with $H_{infty}$ optimization for optical image stabilization (OIS) in mobile phone cameras. The image stabilizer is composed of a horizontal stage constrained by ball bearings and actuated by the magnetic force from voice coil motors. The displacement of the stage is measured by Hall effect sensors. From the OIS frequency response experiment, the transfer function models of the stage and Hall effect sensor were identified. The weight functions were determined considering the tracking performance, noise attenuation, and stability with considerable margins. The $H_{infty}$ optimal controller was executed using closed-loop shaping and limiting the controller order, which should be less than 6 for real-time implementation. The control algorithm was verified experimentally and proved to operate as designed.