The corrosion of alkaline concrete materials exposed to a sulfuric acid environment is becoming more and more prevalent, and its damage assessment is becoming more and more imperative. This study aims to describe the corroded surfaces of concrete with different strength grades (C30, C50, C80) in sulfuric acid environments in terms of their three-dimensional fractal dimension. Three kinds of concrete with varying strength grades, namely C30, C50, and C80, were immersed in a sulfuric acid solution with pH ≈ 0.85 for four distinct corrosion durations, specifically 0, 28, 56, and 165 days, in accelerated corrosion tests. The 3D laser scanning technique was utilized to capture the 3D coordinates of the surface points of the concrete cylinder before and after corrosion. The fractal dimension of concrete’s uneven surface before and after corrosion was computed via the cube covering method, and the mass loss of the concrete specimen was also obtained. The outcomes demonstrate that the three-dimensional fractal dimension provides a new method for characterizing the degree of corrosion deterioration of concrete samples affected by sulfuric acid via laser scanning technology. From the perspective of the appearance, mass loss, and fractal dimension of a rough surface in the sulfuric acid environment at a pH level of approximately 0.85, the degree of the corrosion deterioration of concrete is ranked from high to low as C80 > C50 > C30. These fractal dimensions of the concrete’s corroded surfaces with various strength grades increase rapidly in the initial period. However, as the corrosion time progresses, the growth rate of the corroded surface fractal dimension gradually decelerates and tends towards stability, which accords with the law of exponential function. The widespread belief is that the higher the strength grade of concrete, the better its durability; however, this pattern varies in sulfuric acid corrosive environments. Therefore, based on this research, it is recommended that in extremely acidic environments (i.e., very low pH), more attention should be paid to high-strength grades of concrete.