The invention discloses a pier local scouring protection device with a rotary normal curved surface. The protection device is sleeved on a pier and is approximately in a bell shape, the thickness of the protection device is 0.5-1 m, and the inner surface of the protection device meets an equation of a standard rotary normal curved surface. The protection device is combined with the reciprocating flow characteristic, front impact water flow can be dispersed, the protection device is lifted away from the periphery of the pier in the tangential direction of a convex surface, and water flow impactis reduced; on the other hand, downward scouring water flow can be guided, downward scouring continues to be carried out, the direct scouring effect of the downward scouring water flow on a bed surface is weakened at the position farther away from the pier along the concave surface, and part of front impact water flow can be counteracted; and meanwhile, horseshoe vortexes around the pier are reduced, scouring of the horseshoe vortexes to a pier riverbed is weakened, and meanwhile the stress influence on the pier is small.