With the increasing shortage of natural materials, using steel slag instead of natural sand to prepare concrete has become a promising technology. This study aims to investigate the utilization of unprocessed steel slag in normal- and high-strength concrete, focusing on the effects of steel slag as fine aggregate on the compressive behaviour of concrete. Two types of concrete (normal- and high-strength concrete) and eight replacement percentages of fine aggregate by steel slag (0%, 10%, 20%, 30%, 40%, 60%, 80%, and 100%) are used as the test parameters. A series of axial compression tests are conducted on cylinders of fine steel slag concrete (SSC). The influence of the replacement percentage of steel slag on the stress-strain relation, compressive strength, inflation ratio, elastic modulus, and toughness of normal- and high-strength concrete is analysed. Moreover, the failure mechanism of SSC under compression is discussed. The results show that the compressive strength of SSC is not monotonous with increasing steel slag content and that the use of steel slag as fine aggregate in concrete mixes has a positive effect on the energy absorption capacity. SSC with an optimal steel slag content can exhibit better compressive behaviour compared with normal concrete.