Concrete is one of the most widely used construction materials. There are several methods available to improve its performance, with one of them being the use of high-early-strength admixtures (HESAs). Typical HESAs include calcium nitrate, calcium chloride, and calcium formate (CF). Industrial by-products, such as acetic acid and lime stone sludge (LSS), can be used together to produce calcium acetate (CA), which can subsequently be used as a cementitious HESA. In this study, calcium carbonate and LSS were mixed with cement in weight ratios of 1 : 1, 1 : 1.5, and 1 : 2, and the properties of the as-produced CA were evaluated. CA and CF were mixed with cement in different weight ratios (0, 1, 2, and 3 wt%) to obtain CA- and CF-mortars, respectively. The flow behavior, setting time, pH, and compressive strength of these mortars were evaluated, and their X-ray diffraction patterns were also analyzed. It was found that as the CF content in the CF-mortar increased, the initial strength of the mortar also increased. However, it impaired its long-term strength. On the other hand, when 1% CA was mixed with cement, satisfactory early and long-term strengths were achieved. Thus, CA, which is obtained from industrial by-products, can be an effective HESA.