The physical origin of Type-I (hydrogen-less) superluminous supernovae (SLSNe-I), whose luminosities are 10 to 500 times higher than normal core-collapse supernovae, remains still unknown. Thanks to their brightness, SLSNe-I would be useful probes of distant Universe. For the power source of the light curves of SLSNe-I, radioactive-decays, magnetars, and circumstellar interactions have been proposed, although no definitive conclusions have been reached yet. Since most of light curve studies have been based on simplified semi-analytic models, we have constructed multi-color light curve models by means of detailed radiation hydrodynamical calculations for various mass of stars including very massive ones and large amount of mass loss. We compare the rising time, peak luminosity, width, and decline rate of the model light curves with observations of SLSNe-I and obtain constraints on their progenitors and explosion mechanisms. We particularly pay attention to the recently reported double peaks of the light curves. We discuss how to discriminate three models, relevant models parameters, their evolutionary origins, and implications for the early evolution of the Universe.