An inner main-belt asteroid, P/2010 A2, was discovered on January 6th, 2010. Based on its orbital elements, it is considered that the asteroid belongs to the Flora collisional family, where S-type asteroids are common, whilst 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 (Jewitt et al. 2010; Snodgrass et al. 2010), an alternative idea of ice sublimation was suggested based on the morphological fitting of ground-based images (Moreno et al. 2010). Here, we report a multiband observation of P/2010 A2 made on January 2010 with a 105 cm telescope at the Ishigakijima Astronomical Observatory. Three broadband filters, $g$, $R_c$, and $I_c$, were employed for the observation. The unique multiband data reveals 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$pm$0.046 at the $R_c$-band (650 nm) and 1.131$pm$0.061 at the $I_c$-band (800 nm). We hypothesize that the parent body of P/2010 A2 was originally S-type but was then shattered upon collision into scaterring fresh chondritic particles from the interior, thus forming the dust tail.