Steps effectively dissipate the energy of water along a path and reduce the size of the stilling basin but are rarely used in curved spillways. The shore spillway of a reservoir, which is restricted by topography, must be arranged in a curved shape. At high flow velocity and low water depth, some areas of the base plate of the curved spillway were not covered by the water. The water flow into the stilling basin did not form a submerged hydraulic jump. It was proposed that a step with bottom non-uniform heights be placed in the smooth base plate of the curved spillway to improve these undesirable hydraulic phenomena. A physical model experiment with a length scale of 1:40 verified the feasibility of the curved stepped spillway in engineering. Based on the k-ε model and volume-of-fluid (VOF) method, a three-dimensional numerical model was established, and the reliability of the numerical model was verified by measured data. The main flow region, velocity field, cavitation on a step, and the energy loss rate of steps were discussed. The comparison between a curved spillway with and without steps shows that the steps balance the partial centrifugal force in the curved section, making the water depth of the cross-section evenly distributed, and the base plate was no longer covered by water. The flow pattern on the steps was skimming flow, and the velocity of the flow into the stilling basin was greatly reduced. The elevation of the concave bank of the base plate was raised, resulting in the formation of transverse flow, which in turn constituted a three-dimensional energy dissipation pattern with the longitudinal flow. The energy loss was significantly higher than that of the smooth curved spillway. However, the triangular region near to the concave bank on the base plate experienced negative pressure, and an aeration device in front of the steps was needed.