Artificial reefs (ARs) are one of the key anthropogenic constructs used to restore offshore fishery resources and recover the ecological environment. However, many ARs lose their stability and function due to scour. To ensure the functional effect of ARs, it is of great significance to study the factors causing AR instability, such as burying caused by scour under different flow conditions. In present study, a three-dimensional numerical model is established in FLOW-3D to study the local scour characteristics around an AR in steady currents. Reynolds-averaged Navier–Stokes (RANS) equations, closed with the renormalization group (RNG) k–ɛ turbulence model, are established to simulate a stable flow field around one AR. The simulation results are compared with previous experimental results, exhibiting good agreement. The effects of the opening number and the incident angles of ARs on the scour characteristics, equilibrium scour depth, and maximum scour volume were also investigated. The results indicate that the scour depth and scour volume decreased as the opening number increased. Furthermore, empirical equations are proposed herein based on the numerical results derived for the effects of the AR opening number on the equilibrium scour depth and maximum scour volume. A change in the incident angle affected the bed shear stress at the most-upstream corner of the AR. The greater the bed shear stress was, the more intense the scour was. In this study, we provide theoretical support and practical guidance for the optimized engineering design and construction of ARs.