The international health care system, as well as the Greek health care system under the current climate change problems and the sustainable development goals solutions just begin to understand the impact that environmental and social issues will have on health care services. Greek hospitals and the Greek health care system have the potential not only to adapt to climate change, but also in the process to promote social value, greater social equity and environmental health through sustainable development goals. At the same time, based on a different perspective, social responsibility, environmental management and governance are at the forefront of attention, not only as the most up-to-date characteristics of a hospital strategy, but also in relation to national and international economic policies aiming for better economic results for local communities and stakeholders. In other words, environmental, social and governance issues are today incorporated to sustainable hospital management and have already become part of the Greek Sustainable Health Care System. In this paper the literature review suggests that sustainable health care could be a driver of sustainability in the health care system and specifically in the Greek Hospitals. The empirical research analysis in the Greek hospitals recognized that in the recent years remarkable steps for environmental and social issues have been made. However, according to sustainable management theory, as this is referred in the paper, in order to achieve sustainability in the Greek health care system through sustainable health care management, is necessary to promote, rebuild and adapt the health care system to a concrete holistic sustainable health care management, which is supported and evaluated by the Greek Ministry of Health and the Greek health care market.