The compressive characteristics of the steel-slag concrete were investigated through an experimental test. The term “steel-slag concrete” in this research work was defined as a kind of concrete using steel-slag material as a coarse aggregate replacement. Three types of the steel-slag concretes were examined under compression as follows: XT01, XT02, XT03 with their cement/water ratios of 1.76, 2.00, 2.21, respectively. The coarse aggregate used in producing concrete was steel-slag material, while the fine aggregate was traditional river sand; the ratio of coarse aggregate to fine aggregate was kept constant at a value of 1.98. Firstly, the age-dependent compressive strength of the steel-slag concretes were investigated up to one year; it was clear that the concrete strength increased rapidly in 7 days, then more and more slowly after that. Secondly, the modulus of elasticity and Poisson’s ratio of the steel-slag concretes were explored at the 28-day age. Thirdly, there was an important size and shape effect on the compressive strength of the XT02, and its significance of brittleness in failure was analytically analyzed. Lastly, the effects of water amount added in the XT02 on its compressive strength and slump were evaluated at the 28-day age.