Magnesium alloys are currently used in many structural applications. It is believed that magnesium and its alloys may also find applications in biomedical fields. In this study, a new biomedical magnesium-based alloy, i.e., magnesium–calcium (Mg–Ca) has been designed from biological and metallurgical viewpoints. The microstructure, mechanical and corrosion behaviors of Mg–Ca alloys with varying calcium content were investigated. The results show that a magnesium alloy with 0.6wt.% calcium content (denoted as Mg–0.6Ca) shows good corrosion and mechanical properties. Our preliminary results demonstrate a good potential of this Mg–0.6Ca alloy as a new biomedical material.