If we are able to see an object in a certain color,that means it reflects the color.A blackbody is one which has zero reflectivity.Then how come it is not black always?
Your assumption is incorrect. The color we see is the combination of reflected light, if any, and radiated light. All objects radiate photons of one wavelength or another. All objects absorb photons of one wavelength or another. These two spectral curves (absorption and radiation) are the same, but the spectral power curve of the irradiance obviously depends on external sources, not on the material or temperature of the black body.