The abrasion resistance of concrete has a significant impact on the long-term use of hydraulic drainage structures. At present, improving the abrasion resistance of concrete is mainly achieved by increasing the strength grade. In order to explore the influence of strength grades on the abrasion resistance of concrete, three kinds of concrete with different strength grades, C9060, C9050, and C9040, were designed and produced. The high-speed ring method, underwater method, high-speed underwater method was used to study the anti-suspended load, bed load abrasion of concretes. The results showed that the tensile stress and deformation of concretes could be increased by 20.5%–101.8% and 18.5%–52.3% with the increase of concrete strength grade, but it has little effect on axial tensile modulus. With the increase of curing age, the strength grade could significantly improve the abrasion resistance of the concrete surface to high-speed water suspension by 7.1%–28.0%. The strength grade has little influence on the bed load abrasion resistance of concretes, and the increase in the volume of cementitious material would reduce the bed load abrasion resistance of concretes. Improving strength grade can promote the bonding ability of the cement-aggregate interface, which can significantly improve the impact and abrasion resistance of concrete.