In the past several decades, the standard cosmological model has been established and its parameters have been measured to a high precision, while there are still many fundamental questions in cosmology; such as the physics in the very early universe, the origin of the cosmic acceleration, and the nature of dark matter. The forthcoming radio telescope, the Square Kilometre Array (SKA), which will be the world's largest, will be able to open a new frontier in cosmology and will be one of the most powerful tools for cosmology in the coming decade. The cosmological surveys conducted by the SKA would have the potential not only to answer these fundamental questions but also deliver precision cosmology. In this article we briefly review the role of the SKA from the viewpoint of modern cosmology. The cosmological science led by the SKA-Japan Consortium (SKA-JP) Cosmology Science Working Group is also discussed.