The accurate measurement of the 3D dose distribution of carbon-ion beams is essential for safe carbon-ion therapy. Although ionization chambers scanned in a water tank or air are conventionally used for this purpose, these measurement methods are time-consuming. We thus developed a rapid 3D dose-measurement tool that employs a silver-activated zinc sulfide (ZnS) scintillator with lower linear energy transfer (LET) dependence than gadolinium-based (Gd) scintillators; this tool enables the measurement of carbon-ion beams with small corrections. A ZnS scintillator sheet was placed vertical to the beam axis and installed in a shaded box. Scintillation images produced by incident carbon-ions were reflected with a mirror and captured with a charge-coupled device (CCD) camera. A 290 MeV/nucleon mono-energetic beam and spread-out Bragg peak (SOBP) carbon-ion passive beams were delivered at the Gunma University Heavy Ion Medical Center. A water tank was installed above the scintillator with the water level remotely adjusted to the measurement depth. Images were recorded at various water depths and stacked in the depth direction to create 3D scintillation images. Depth and lateral profiles were analyzed from the images. The ZnS-scintillator-measured depth profile agreed with the depth dose measured using an ionization chamber, outperforming the conventional Gd-based scintillator. Measurements were realized with smaller corrections for a carbon-ion beam with a higher LET than a proton. Lateral profiles at the entrance and the Bragg peak depths could be measured with this tool. The proposed method would make it possible to rapidly perform 3D dose-distribution measurements of carbon-ion beams with smaller quenching corrections.