An inner main-belt asteroid, P/2010 A2, was discovered on 2010 January 6. Based on its orbital elements, it is considered that the asteroid belongs to the Flora collisional family, where S-type asteroids are common, while showing a comet-like dust tail. Although analysis of images taken by the Hubble Space Telescope and Rosetta spacecraft suggested that the dust tail resulted from a recent head-on collision between asteroids, an alternative idea of ice sublimation was suggested based on the morphological fitting of ground-based images. Here, we report a multiband observation of P/2010 A2 made on 2010 January with a 105 cm telescope at the Ishigakijima Astronomical Observatory. Three broadband filters, g', Rc , and Ic , were employed for the observation. The unique multiband data reveal that the reflectance spectrum of the P/2010 A2 dust tail resembles that of an Sq-type asteroid or that of ordinary chondrites rather than that of an S-type asteroid. Due to the large error of the measurement, the reflectance spectrum also resembles the spectra of C-type asteroids, even though C-type asteroids are uncommon in the Flora family. The reflectances relative to the g' band (470 nm) are 1.096 ± 0.046 at the Rc band (650 nm) and 1.131 ± 0.061 at the Ic band (800 nm). We hypothesize that the parent body of P/2010 A2 was originally S-type but was then shattered upon collision into scattering fresh chondritic particles from the interior, thus forming the dust tail.