Thermal energy storage (TES) systems for concentrated solar power plants are essential for the convenience of renewable energy sources in terms of energy dispatchability, economical aspects and their larger use. TES systems based on the use of concrete have been demonstrated to possess good heat exchange characteristics, wide availability of the heat storage medium and low cost. Therefore, the purpose of this work was the development and characterization of a new concrete-based heat storage material containing a concrete mix capable of operating at medium–high temperatures with improved performance. In this work, a small amount of shape-stabilized phase change material (PCM) was included, thus developing a new material capable of storing energy both as sensible and latent heat. This material was therefore characterized thermally and mechanically and showed increased thermal properties such as stored energy density (up to +7%, with a temperature difference of 100 °C at an average operating temperature of 250 °C) when 5 wt% of PCM was added. By taking advantage of these characteristics, particularly the higher energy density, thermal energy storage systems that are more compact and economically feasible can be built to operate within a temperature range of approximately 150–350 °C with a reduction, compared to a concrete-only based thermal energy storage system, of approximately 7% for the required volume and cost.