Demolishing concrete building usually produces huge amounts of remains and wastes worldwide that have promising possibilities to be utilized as coarse aggregate for new mixes of concrete. High numbers of structures around the world currently need to be removed for several reasons, such as reaching the end of the expected life, to be replaced by new investments, or were not built by the local and international standards. Maintaining or removal of such structures leads to large quantities of concrete ruins. Reusing these concrete wastes will help in saving landfill spaces in addition to more sustainability in natural resources. The objective of this study is to investigate the possibility of using old recycled concrete as coarse aggregate to make new concrete mixes, and its effect on the evolution of the compressive strength of the new concrete mixes. Core samples for demolished concrete were tested to determine its compressive strength. The core test results can be thought of as aggregate properties for the new concrete. Then, the compressive strength and splitting tensile strength of the new recycled aggregate concrete (RAC) were determined experimentally by casting a cubes and cylinders, respectively. It was found that the evolution of compressive strength of recycled aggregate concrete is similar in behavior to the concrete with natural aggregate, except that it is about 10% lower in values. It was also seen that water absorption for recycled aggregate is noticeably higher than that for natural aggregate, and should be substituted for in the mix design.