The fact that no there exists yet an absolute treatment or vaccine for COVID-19, which was declared as a pandemic by the World Health Organization (WHO) in 2020, makes very important spread out over time of the epidemic in order to burden less on hospitals and prevent collapsing of the health care system. This case is a consequence of limited resources and is valid for all countries in the world facing with this serious threat. Slowing the speed of spread will probably make that the outbreak last longer, but it will cause lower total death count. In this study, a new SEIR epidemic model formed by taking into account the impact of health care capacity has been examined and local and global stability of the model has been analyzed. In addition, the model has been also supported by some numerical simulations.